diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index b582cc75..4e737a33 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -8,6 +8,7 @@ debug messages to stdout, simply call :func:`set_debug_function` without
 arguments.
 """
 from pathlib import Path
+from typing import Any
 
 import parso
 from parso.python import tree
@@ -338,7 +339,7 @@ class Script:
             fuzzy=fuzzy,
         )
 
-    def complete_search(self, string, **kwargs):
+    def complete_search(self, string, **kwargs) -> list[Any]:
         """
         Like :meth:`.Script.search`, but completes that string. If you want to
         have all possible definitions in a file you can also provide an empty
diff --git a/jedi/inference/star_args.py b/jedi/inference/star_args.py
index 0d8a132b..2a9dd6b1 100644
--- a/jedi/inference/star_args.py
+++ b/jedi/inference/star_args.py
@@ -11,9 +11,10 @@ This means for example in this case::
 The signature here for bar should be `bar(b, c)` instead of bar(*args).
 """
 from inspect import Parameter
+from typing import Sequence
 
 from jedi.inference.utils import to_list
-from jedi.inference.names import ParamNameWrapper
+from jedi.inference.names import ParamNameWrapper, AnonymousParamName
 from jedi.inference.helpers import is_big_annoying_library
 
 
@@ -94,7 +95,11 @@ def _remove_given_params(arguments, param_names):
 
 
 @to_list
-def process_params(param_names, star_count=3):  # default means both * and **
+def process_params(param_names: Sequence[AnonymousParamName | ParamNameFixedKind], star_count=3, already_used=None):
+    # start_count=3 means both * and **
+    if already_used is None:
+        already_used = set()
+
     if param_names:
         if is_big_annoying_library(param_names[0].parent_context):
             # At first this feature can look innocent, but it does a lot of
@@ -112,14 +117,22 @@ def process_params(param_names, star_count=3):  # default means both * and **
     original_arg_name = None
     original_kwarg_name = None
     for p in param_names:
+        def is_recursion():
+            is_recursion = p.tree_name in already_used
+            if not is_recursion:
+                already_used.add(p.tree_name)
+            return is_recursion
+
         kind = p.get_kind()
         if kind == Parameter.VAR_POSITIONAL:
             if star_count & 1:
-                arg_callables = _iter_nodes_for_param(p)
+                if not is_recursion():
+                    arg_callables = _iter_nodes_for_param(p)
                 original_arg_name = p
         elif p.get_kind() == Parameter.VAR_KEYWORD:
             if star_count & 2:
-                kwarg_callables = list(_iter_nodes_for_param(p))
+                if not is_recursion():
+                    kwarg_callables = list(_iter_nodes_for_param(p))
                 original_kwarg_name = p
         elif kind == Parameter.KEYWORD_ONLY:
             if star_count & 2:
@@ -157,7 +170,7 @@ def process_params(param_names, star_count=3):  # default means both * and **
                     list(_remove_given_params(
                         arguments,
                         signature.get_param_names(resolve_stars=False)
-                    )), new_star_count):
+                    )), new_star_count, already_used):
                 if p.get_kind() == Parameter.VAR_KEYWORD:
                     kwarg_names.append(p)
                 elif p.get_kind() == Parameter.VAR_POSITIONAL:
@@ -190,7 +203,7 @@ def process_params(param_names, star_count=3):  # default means both * and **
                     list(_remove_given_params(
                         arguments,
                         signature.get_param_names(resolve_stars=False)
-                    )), star_count=2):
+                    )), star_count=2, already_used=already_used):
                 if p.get_kind() == Parameter.VAR_KEYWORD:
                     kwarg_names.append(p)
                 elif p.get_kind() == Parameter.KEYWORD_ONLY:
diff --git a/jedi/inference/utils.py b/jedi/inference/utils.py
index 2f8d41f1..161f0ba8 100644
--- a/jedi/inference/utils.py
+++ b/jedi/inference/utils.py
@@ -2,6 +2,7 @@
 import functools
 import re
 import os
+from typing import ParamSpec, TypeVar, Callable, Iterable
 
 
 _sep = os.path.sep
@@ -10,8 +11,11 @@ if os.path.altsep is not None:
 _path_re = re.compile(r'(?:\.[^{0}]+|[{0}]__init__\.py)$'.format(re.escape(_sep)))
 del _sep
 
+P = ParamSpec("P")
+T = TypeVar("T")
 
-def to_list(func):
+
+def to_list(func: Callable[P, Iterable[T]]) -> Callable[P, list[T]]:
     def wrapper(*args, **kwargs):
         return list(func(*args, **kwargs))
     return wrapper
diff --git a/test/test_api/test_signatures.py b/test/test_api/test_signatures.py
index bf254185..e532baaf 100644
--- a/test/test_api/test_signatures.py
+++ b/test/test_api/test_signatures.py
@@ -1,3 +1,5 @@
+from textwrap import dedent
+
 import pytest
 
 _tuple_code = 'from typing import Tuple\ndef f(x: Tuple[int]): ...\nf'
@@ -69,3 +71,28 @@ def test_param_kind_and_name(code, index, param_code, kind, Script):
 def test_staticmethod(Script):
     s, = Script('staticmethod(').get_signatures()
     assert s.to_string() == 'staticmethod(f: Callable[_P, _R_co], /)'
+
+
+def test_recursive_star_kwargs_do_not_recurse(Script):
+    # From #2085
+    code = dedent('''
+        def test(x, **kwargs):
+            if isinstance(x, int):
+                return test((x,), **kwargs)
+        test(
+        ''')
+    script = Script(code)
+    script.complete()
+    signature, = script.get_signatures()
+    assert signature.to_string() == 'test(x, **kwargs)'
+
+    code = dedent('''
+        def test(x, *args, **kwargs):
+            if isinstance(x, int):
+                return test((x,), *args, **kwargs)
+        test(
+        ''')
+    script = Script(code)
+    script.complete()
+    signature, = script.get_signatures()
+    assert signature.to_string() == 'test(x, *args, **kwargs)'