diff --git a/mypy/checkexpr.py b/mypy/checkexpr.py
index f9fbd53866da..513065013958 100644
--- a/mypy/checkexpr.py
+++ b/mypy/checkexpr.py
@@ -1426,6 +1426,7 @@ def check_callable_call(
             need_refresh = any(
                 isinstance(v, (ParamSpecType, TypeVarTupleType)) for v in callee.variables
             )
+            old_callee = callee
             callee = freshen_function_type_vars(callee)
             callee = self.infer_function_type_arguments_using_context(callee, context)
             if need_refresh:
@@ -1440,7 +1441,7 @@ def check_callable_call(
                     lambda i: self.accept(args[i]),
                 )
             callee = self.infer_function_type_arguments(
-                callee, args, arg_kinds, formal_to_actual, context
+                callee, args, arg_kinds, formal_to_actual, context, old_callee
             )
             if need_refresh:
                 formal_to_actual = map_actuals_to_formals(
@@ -1730,6 +1731,7 @@ def infer_function_type_arguments(
         arg_kinds: list[ArgKind],
         formal_to_actual: list[list[int]],
         context: Context,
+        unfreshened_callee_type: CallableType,
     ) -> CallableType:
         """Infer the type arguments for a generic callee type.
 
@@ -1773,6 +1775,28 @@ def infer_function_type_arguments(
                     callee_type, args, arg_kinds, formal_to_actual, inferred_args, context
                 )
 
+            return_type = get_proper_type(callee_type.ret_type)
+            if isinstance(return_type, CallableType):
+                # fixup:
+                # def [T] () -> def (T) -> T
+                # into
+                # def () -> def [T] (T) -> T
+                for i, argument in enumerate(inferred_args):
+                    if isinstance(get_proper_type(argument), UninhabitedType):
+                        # un-"freshen" the type variable :^)
+                        variable = unfreshened_callee_type.variables[i]
+                        inferred_args[i] = variable
+
+                        # handle multiple type variables
+                        return_type = return_type.copy_modified(
+                            variables=[*return_type.variables, variable]
+                        )
+
+                callee_type = callee_type.copy_modified(
+                    # Question: am I allowed to assign the get_proper_type'd thing?
+                    ret_type=return_type
+                )
+
             if (
                 callee_type.special_sig == "dict"
                 and len(inferred_args) == 2
diff --git a/test-data/unit/check-inference.test b/test-data/unit/check-inference.test
index 166e173e7301..582423f39c4e 100644
--- a/test-data/unit/check-inference.test
+++ b/test-data/unit/check-inference.test
@@ -3105,7 +3105,8 @@ T = TypeVar('T')
 
 def f(x: Optional[T] = None) -> Callable[..., T]: ...
 
-x = f()  # E: Need type annotation for "x"
+# Question: Is this alright?
+x: Callable[..., T] = f()
 y = x
 
 [case testDontNeedAnnotationForCallable]
diff --git a/test-data/unit/check-parameter-specification.test b/test-data/unit/check-parameter-specification.test
index fe66b18fbfea..21c2e7c7e850 100644
--- a/test-data/unit/check-parameter-specification.test
+++ b/test-data/unit/check-parameter-specification.test
@@ -1520,3 +1520,28 @@ def identity(func: Callable[P, None]) -> Callable[P, None]: ...
 @identity
 def f(f: Callable[P, None], *args: P.args, **kwargs: P.kwargs) -> None: ...
 [builtins fixtures/paramspec.pyi]
+
+[case testParamSpecificationSurvivesCall]
+# https://github.com/python/mypy/issues/12595
+from typing import TypeVar, Callable
+from typing_extensions import Concatenate, ParamSpec
+
+T = TypeVar('T')
+U = TypeVar('U')
+P = ParamSpec('P')
+
+def t(f: Callable[P, T]) -> Callable[P, T]: ...
+
+def pop_off(
+    transform: Callable[Concatenate[T, P], U]
+) -> Callable[P, Callable[[T], U]]: ...
+
+u = pop_off(t)
+reveal_type(u)  # N: Revealed type is "def [P, T] () -> def (def (*P.args, **P.kwargs) -> T`-2) -> def (*P.args, **P.kwargs) -> T`-2"
+
+@u()
+def f(x: int) -> None: ...
+
+reveal_type(f)  # N: Revealed type is "def (x: builtins.int)"
+f(0)
+[builtins fixtures/paramspec.pyi]