Use NSMenuDelegate for browser action overflow menu to update it upon opening.

chrome/browser/ui/cocoa/extensions/browser_action_button.mm

 // Copyright (c) 2012 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.
 
 #import "chrome/browser/ui/cocoa/extensions/browser_action_button.h"
 
 #include <algorithm>
 #include <cmath>
 
 #include "base/logging.h"
@@ skipping 13 matching lines @@
 #import "third_party/GTM/AppKit/GTMNSAnimation+Duration.h"
 #include "ui/base/resource/resource_bundle.h"
 #include "ui/gfx/canvas_skia_paint.h"
 #include "ui/gfx/image/image.h"
 #include "ui/gfx/rect.h"
 #include "ui/gfx/scoped_ns_graphics_context_save_gstate_mac.h"
 #include "ui/gfx/size.h"
 
 using extensions::Extension;
 
-NSString* const kBrowserActionButtonUpdatedNotification =
-    @"BrowserActionButtonUpdatedNotification";
-
 NSString* const kBrowserActionButtonDraggingNotification =
     @"BrowserActionButtonDraggingNotification";
 NSString* const kBrowserActionButtonDragEndNotification =
     @"BrowserActionButtonDragEndNotification";
 
 static const CGFloat kBrowserActionBadgeOriginYOffset = 5;
 
 namespace {
 const CGFloat kAnimationDuration = 0.2;
 }  // anonymous namespace
@@ skipping 223 matching lines @@
   } else if (defaultIcon_) {
     [self setImage:defaultIcon_];
   }
 
   [[self cell] setTabId:tabId_];
 
   bool enabled = extension_->browser_action()->GetIsVisible(tabId_);
   [self setEnabled:enabled ? YES : NO];
 
   [self setNeedsDisplay:YES];
-
-  [[NSNotificationCenter defaultCenter]
-      postNotificationName:kBrowserActionButtonUpdatedNotification
-      object:self];
 }
 
 - (BOOL)isAnimating {
   return [moveAnimation_ isAnimating];
 }
 
 - (NSImage*)compositedImage {
   NSRect bounds = [self bounds];
   NSImage* image = [[[NSImage alloc] initWithSize:bounds.size] autorelease];
   [image lockFocus];
@@ skipping 35 matching lines @@
 }
 
 - (void)drawInteriorWithFrame:(NSRect)cellFrame inView:(NSView*)controlView {
   gfx::ScopedNSGraphicsContextSaveGState scopedGState;
   [super drawInteriorWithFrame:cellFrame inView:controlView];
   cellFrame.origin.y += kBrowserActionBadgeOriginYOffset;
   [self drawBadgeWithinFrame:cellFrame];
 }
 
 @end