To get all that stubborn gunk off the bottom of your pretty pans, there's a vinegar trick you can use. Opt for the same technique you'd use to deglaze a pan, and use white vinegar.
Simply pour a little vinegar in the dirty pan and heat it up. Scraping gently with a wooden spoon, the offensive brown bits lift right off. Follow up this trick with a little soap and water in the sink, plus a good rinse, and you've got a sparkling clean pan that you can practically see your reflection in.
Watch this stop-motion video to see this tip in action.