Step 11. In a large bowl, combine the ground steak with the salt, several grinds of pepper, the powdered onion and garlic powders, beaten egg, Worcestershire sauce, soy sauce and Parmesan cheese. Mix the ingredients together until combined, being careful not to overwork. Cover and refrigerate the meat for 30 to 40 minutes.
Step 22. Divide the mixture and form into 6 patties, making sure to indent the center of each patty so it does not plump up on the grill. Crack a little more black pepper over each patty and refrigerate until ready to grill.
Step 11. Halve the onions and thinly slice. Place the onions in a bowl and toss with enough olive oil to lightly coat.
Step 22. Warm a large cast-iron skillet or Dutch oven over medium heat. Add one-fourth cup olive oil, and when the oil just starts to shimmer, add the onions. Cook the onions over medium heat, stirring infrequently.
Step 33. After about 20 minutes, stir in one-half teaspoon salt and a few grinds of pepper, along with the sugar. Cook an additional 30 minutes, stirring occasionally.
Step 44. Reduce the heat to low and continue to cook until the onions begin to caramelize, and their volume has reduced by more than half, 45 minutes to an hour. Remove from heat and remove the onions, leaving any leftover bits and juices in the pan (the pan will be used to make the steak sauce).
Step 1In a large cast-iron skillet, melt the butter and oil over medium-low heat. Add the shallot and garlic, cooking until the shallot is nearly translucent, 6 to 8 minutes. Stir in the mushrooms and season with one teaspoon salt and several grinds of pepper, or to taste. Cook, stirring occasionally, for 1 to 2 hours until the mushrooms are soft and reduced in volume by over half. Add the wine and, off heat, carefully light a match over the wine to burn off the alcohol. Continue cooking for another 30 minutes, stirring frequently.
Step 11. Heat the grill.
Step 22. Halve the burger buns and brush the bottoms with steak sauce.
Step 33. Grill the burgers, brushing the tops with steak sauce after they are flipped. Just before the burgers are finished, add the buns to lightly toast. When the burgers are done, remove and rest under foil for about 10 minutes.
Step 44. Add a large scoop of mushrooms to the bottom of each bun. Place a burger over the mushrooms and top with caramelized onions, then the bun top.