Task Manager should listen to WebContentsObserver::RenderFrameCreated.

content/public/browser/render_process_host_utils.h

+// Copyright 2017 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#ifndef CONTENT_PUBLIC_BROWSER_RENDER_PROCESS_HOST_UTILS_H_
+#define CONTENT_PUBLIC_BROWSER_RENDER_PROCESS_HOST_UTILS_H_
+
+#include "base/callback.h"
+#include "content/common/content_export.h"
+
+namespace content {
+
+class RenderProcessHost;
+
+// Posts |task|, if |render_process_host| is ready or when it becomes ready (see
+// RenderProcessHost::IsReady method).  The |task| might not run at all (e.g. if
+// |render_process_host| is destroyed before becoming ready).  This function can
+// only be called on the browser's UI thread (and the |task| will be posted back
+// on the UI thread).
+CONTENT_EXPORT void PostTaskWhenRenderProcessHostIsReady(
+    RenderProcessHost* render_process_host,
+    base::OnceClosure task);

[Łukasz Anforowicz, 2017/05/06 00:16:45]

Also - please shout if you think I should add a test specifically targeting the
newly added function.  I was kind of on the fence whether the task manager
browser tests are providing sufficient test coverage for the new function (they
probably are, but are doing this in a rather indirect way).

+
+}  // namespace content
+
+#endif  // CONTENT_PUBLIC_BROWSER_RENDER_PROCESS_HOST_UTILS_H_