Cook your onions in the butter, in a saucepan over low heat. Throw your thyme sprigs in whole and let them cook with the onions until they are soft and golden. It may take an hour or so. Season to taste with salt and a splash of vinegar (if you want).
Make your mayo - add a grated (or very finely minced) clove of garlic to your favorite mayo, and season to taste with salt and lots of pepper. If you’re worried about the garlic being too strong, use half a clove.
Prep your lettuce, tomato, burger buns, and cheese, set them aside.
Prep your beef by breaking it up with your hands in a bowl, add worcestershire and about 1/2 teaspoon of salt per pound of beef. Form the beef into 1/4 or 1/3 pound patties and set them aside, leaving a tiny piece out to cook and taste later.
Heat your pan or grill over medium-high to high heat. Fry up your tester bite of burger, adjust seasoning if necessary. Get your burgers in the pan and let them cook until half-done on the first side. Flip them once, and add your cheese to the other side. Cook to desired doneness.
Assemble burgers - bun on the bottom, followed by onions, patty with melted cheese, tomato, lettuce, garlic mayo, and finally the top bun. Remember: if you don't do it in that order I won't know or care.