Oklahoma Fried Onion Burgers!

I actually have similar techniquet for my burgers. When grilling, I meld my burgers with a slice of onion (I hand cut them and am pretty poor with a knife, so the slices are almost as thick as the domed patty) before putting them over the heat onion down. They brown from indirect heat and from direct when I flip them. When cooking inside, I dice the union. For best taste, I’ll heat the heavy baking dish and oil to the oven’s max, pull out the dish, quickly put on the burgers and onions (again, onions down, either by putting the onions on top and flipping them onto the dish or putting the burgers on top of the onions and sliding the spatula under both), put it right back in, and set the oven to a normal cooking temp, but this sends oil spitting everywhere. Lately, I just put the onions in the dish, put both in the cold oven, and let both preheat to the cooking temp. The surround heating of the oven and possibly a bit of broiler action puts on a nice crust.

Ingredients:
1 large onion, peeled, halved and thinly sliced
salt and pepper
1 lb ground beef
1 tablespoon butter
1 tablespoon vegetable oil
4-8 slices American cheese
Mayo, mustard and pickles, for serving
4 hamburger buns, toasted

HOW TO MAKE:
Combine the onion slices and 1 teaspoon of salt in a bowl and toss to combine. Transfer the onions to a colander and let sit for 30 minutes, tossing occasionally. Transfer the onions to a clean dish towel, gather the edges together and squeeze out as much liquid as you can from the onions. Do this over the sink or a large bowl since the onions will have quite a bit of liquid in them.
Divide the onions into 4 separate mounds on a rimmed baking sheet. Form the beef into 4 lightly packed balls. Place the beef balls on top of the onion mounds and flatten the beef firmly (use your palm) so the onion adheres to the beef. The patties should measure 4 inches in diameter. Season the beef generously with salt and pepper.
Melt the butter with the oil in a 12-inch skillet over medium heat. Using a large spatula, transfer the patties to the skillet, onion side down. Cook for 6-8 minutes, until the onions turn a deep golden brown and begin to crisp around the edges. Flip the burgers, then increase the heat to high and cook until well browned on the second side, about 2 minutes.
Add 1 or 2 slices of cheese to each burger and allow to melt. Add mayo, mustard and pickles to the top buns, then place each burger on a bottom buns. Serve immediately.