6 to 8 sweet onions, preferably Maui
1/4 cup extra-virgin olive oil, plus more as needed
2 1/2 teaspoons salt, divided
Freshly ground black pepper, to taste
2 teaspoons sugar
2 1/2 pounds ground rib-eye steak (grind yourself, or have butcher grind for you)
3/4 teaspoon each: powdered onion and garlic, or to taste
1 egg, beaten
4 teaspoons Worcestershire sauce
2 teaspoons soy sauce
2 tablespoons grated Parmesan cheese
6 soft but dense burger buns or rolls
Steak sauce of choice, as needed
Mushroom Reduction (recipe follows)

Halve the onions, peel and thinly slice. Place onions in a bowl and toss with enough of the olive oil to lightly coat.

Warm a large, cast-iron skillet or Dutch oven over medium heat. Add the 1/4 cup olive oil, and when oil just starts to shimmer, add onions. Cook onions over medium heat, stirring infrequently.

After about 20 minutes, stir in 1/2 teaspoon of the salt and a few grinds of the pepper, along with the sugar. Cook an additional 30 minutes, stirring occasionally.

Reduce heat to low and continue to cook until onions begin to caramelize, and their volume has reduced by more than half, for 45 minutes to an hour.

In a large bowl, combine the ground steak with remaining 2 teaspoons salt, several grinds of pepper, the powdered onion and garlic, beaten egg, Worcestershire sauce, soy sauce and Parmesan cheese. Mix ingredients together until combined, being careful not to overwork. Cover and refrigerate meat for 30 to 40 minutes.

Divide mixture and form into 6 patties, making sure to indent center of each so it does not plump up on grill. Crack a little more black pepper over each patty and refrigerate until ready to grill.

When ready to cook burgers, heat grill. Halve the burger buns and brush bottoms with the steak sauce.

Grill burgers, brushing tops with steak sauce after they are flipped. Just before burgers are finished, add buns to lightly toast. When burgers are done, remove and rest under foil for about 10 minutes.

Add a large scoop of the Mushroom Reduction to bottom of each bun. Place burgers over mushrooms and top with caramelized onions, then bun tops. Makes 6 servings.

MUSHROOM REDUCTION: In a large, cast-iron skillet over medium-low heat, melt 2 tablespoons butter into 2 tablespoons extra-virgin olive oil. Add 1 large, peeled and diced shallot and 3 peeled and smashed garlic cloves; cook until shallot is nearly translucent, for 6 to 8 minutes. Stir in 2 pounds thinly sliced cremini mushrooms and season with 1 teaspoon salt and several grinds of black pepper, or to taste. Cook, stirring occasionally, for 1 to 2 hours until mushrooms are soft and reduced in volume by over half. Add 2 tablespoons Madeira wine and, off heat, carefully light a match over wine to burn off alcohol. Continue cooking for another 30 minutes, stirring frequently.

— Recipe from Christopher Lucchese, Echo Park, Los Angeles.