aiohttp memory leak when middleware is enabled when requesting a resource with a non-allowed method

@@ -54,6 +54,7 @@
     MaskDomain,
     MatchedSubAppResource,
     PrefixedSubAppResource,
+    SystemRoute,
     UrlDispatcher,
 )
 
@@ -79,7 +80,6 @@
 _Resource = TypeVar("_Resource", bound=AbstractResource)
 
 
-@lru_cache(None)
 def _build_middlewares(
     handler: Handler, apps: Tuple["Application", ...]
 ) -> Callable[[Request], Awaitable[StreamResponse]]:
@@ -90,6 +90,9 @@ def _build_middlewares(
     return handler
 
 
+_cached_build_middleware = lru_cache(maxsize=1024)(_build_middlewares)
+
+
 class Application(MutableMapping[Union[str, AppKey[Any]], Any]):
     ATTRS = frozenset(
         [
@@ -544,8 +547,13 @@ async def _handle(self, request: Request) -> StreamResponse:
         handler = match_info.handler
 
         if self._run_middlewares:
-            if not self._has_legacy_middlewares:
-                handler = _build_middlewares(handler, match_info.apps)
+            # If its a SystemRoute, don't cache building the middlewares since
+            # they are constructed for every MatchInfoError as a new handler
+            # is made each time.
+            if not self._has_legacy_middlewares and not isinstance(
+                match_info.route, SystemRoute
+            ):
+                handler = _cached_build_middleware(handler, match_info.apps)
             else:
                 for app in match_info.apps[::-1]:
                     for m, new_style in app._middlewares_handlers:  # type: ignore[union-attr]

@@ -0,0 +1 @@
+Fixed system routes polluting the middleware cache -- by :user:`bdraco`.

@@ -1,10 +1,11 @@
 import re
-from typing import Any
+from typing import Any, NoReturn
 
 import pytest
 from yarl import URL
 
-from aiohttp import web
+from aiohttp import web, web_app
+from aiohttp.pytest_plugin import AiohttpClient
 from aiohttp.typedefs import Handler
 
 
@@ -520,3 +521,27 @@ async def call(self, request, handler: Handler):
     assert 201 == resp.status
     txt = await resp.text()
     assert "OK[new style middleware]" == txt
+
+
+async def test_middleware_does_not_leak(aiohttp_client: AiohttpClient) -> None:
+    async def any_handler(request: web.Request) -> NoReturn:
+        assert False
+
+    class Middleware:
+        @web.middleware
+        async def call(
+            self, request: web.Request, handler: Handler
+        ) -> web.StreamResponse:
+            return await handler(request)
+
+    app = web.Application()
+    app.router.add_route("POST", "/any", any_handler)
+    app.middlewares.append(Middleware().call)
+
+    client = await aiohttp_client(app)
+
+    web_app._cached_build_middleware.cache_clear()
+    for _ in range(10):
+        resp = await client.get("/any")
+        assert resp.status == 405
+    assert web_app._cached_build_middleware.cache_info().currsize < 10