You did ask for Chemistry, although of the kitchen variety. If you want Biochemistry of the TMI variety, I’ve got that.
Cooked eggs are denatured proteins. Stomach acid, as well as containing Hydrochloric Acid, also contains enzymes that break down proteins, denatured or otherwise.
How do you get those enzymes in a usefully pure form? That’s where the TMI comes in. Here’s my best idea for a kitchen chemist’s resources:
[spoiler]The night before cooking eggs, on an empty stomach, drink heavily. Preferably vodka or some other clear hard liquor, no mixers or chasers, other than plain water. Tap is fine, or your favorite bottled water will do, too. Drink enough to get completely hammered, but not so you wind up hospitalized for alcohol poisoning. If you vomit, don’t bother saving it. Feel free to pray at the porcelain altar. You don’t want to save that batch. Just drink a bit more booze to replace what you lost. Go sleep it off.
The next morning, when you are totally hung over, and feeling really sick to your stomach, drink (rapidly, within about 15 minutes or less) about a quart of water, with about 2 tsp of salt in it. Hold it in as long as possible before you yack that up. Collect it in a convenient container (no, not the toilet), as that’s the batch you want to save. It should taste like you ralphed salty vinegar. If not, you’ll have to skip the eggs for breakfast. You probably didn’t hold it in long enough. If it did taste right, coming up, you have a good dose of HCl and digestive enzymes in there. It should work fine.
Cook your eggs normally, then put the (now roughly room-temperature, although if you can keep everything at about 37deg C, it’ll work better) watery vomit into the pan. Leave soak as you eat your eggs. After about 2 hours of soak time have passed, dump out the [del]vomit[/del] enzyme/acid solution, and wash the pan, normally. It should clean up easily if you got enough of the digestive enzymes in your [del]barf[/del] cleaning solution.[/spoiler]
There ya go. Kitchen Chemistry at it’s worst! Enjoy!