Make the homemade buns by hydrating 2.5 teaspoons of yeast into 1/2 cup of water and 1/2 cup of milk. Mix together 3.5 cups of flour, 1.5 teaspoons of salt, and 1 tablespoon of sugar. Add 3 tablespoons of vegetable oil, then the yeasty milky mixture, followed by an egg and an egg yolk. Mix until smooth and supple, shape into a ball, and let it rise for one hour. Divide into 8 pieces, shape into balls, and let proof for 30 minutes. Brush with beaten egg and bake at 375°F for 15-18 minutes. Brush with melted butter and let cool on a wire rack.
Make the sauce by searing diced sweet onion in vegetable oil until lightly charred and translucent. Mix together mayonnaise, ketchup, yellow mustard, diced dill pickle, and seared onion. Season with salt and pepper to taste.
Divide the ground beef into 8 even pieces and shape into balls. Sear each ball in a hot pan, pressing down with a spatula until round and a little thinner than half an inch. Season with salt and pepper, flip, and add a slice of cheddar or American cheese. Sear for one more minute and melt the cheese.
Toast the homemade buns with butter or vegetable oil. Sauce both cut sides generously and add the first patty to the bun. Repeat with the second patty and a slice of the other cheese. Top with a dollop of sauce and the other half of the bun.
Enjoy your homemade gourmet burger!
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