I'm not gonna lie, this is pretty much a rip off of AB's burger recipe, and he did it first, but I have a few changes that I feel make a pretty big difference. Among other things, I omit the pickles because I'd rather enjoy them on the side than in the burger, and the pickle/mustard layer tends to be a place for things to slide apart.
For a burger you'll need:
1/4 lb of 80/20 ground beef
1-2 t worchestershire
garlic powder to taste, or minced garlic to taste
a dash of cayenne or to taste
liberal doses of both salt and pepper
1 hamburger bun
smear of mayonnaise
2 slices American cheese
a little bacon grease or butter
a thin spread of hot sauce, preferably this if you can take the heat, see variation
Oil to fry
Mix together the meat ingredients and let sit for at least 30 minutes for the flavors to meld at room temperature, then crush them out in to a 5-6 inch round on a cutting board or the like where they can be scraped, in that general shape, in to the oil for frying.
While the flavors are melding heat oil for frying to 325 F. While the oil is heating melt the grease/butter in a skillet and toast both halves of the bun. When toasted apply a thin coating of mayo to the bottom bun, then apply the cheese to both buns.
Carefully slide the patty off of the cutting board straight in to the oil and fry for 70-75 seconds to get a nice crispy outer layer while staying moist. Immediately remove to some paper towels to remove grease, then place on the bottom bun. Apply a thin smear of hot sauce, and top with the upper bun so the heat of the patty will ensure the cheese finishes melting.
Variation: replace the top slice of American cheese with blue cheese, and exchange the hot sauce with the milder wing sauce
Note: I don't believe in lettuce and tomato on burgers, or pickles. Those belong in a salad on the side, if they're in season (which they probably aren't). Perfect your meat, perfect your salad, and serve the two side by side. I'd suggest some braised fennel in the winter when greens are crappy. A tomato should never been included except in the best of local tomato season in the late summer.