In a large mixing bowl, gently add the ground beef brisket, breaking it up slightly with your fingers without compressing it too much.

Sprinkle the kosher salt, freshly ground black pepper, garlic powder, and onion powder evenly over the brisket.

Drizzle the Worcestershire sauce over the seasoned meat.

Using your hands, gently fold the seasonings and Worcestershire sauce into the brisket just until combined, being careful not to overmix so the burgers stay tender.

Divide the mixture into 4 equal portions and lightly shape each portion into a patty about 3/4 inch thick, slightly wider than your brioche buns.

Using your thumb, press a shallow indentation into the center of each patty to help them cook evenly and prevent doming.

Place the shaped patties on a plate or tray, cover, and refrigerate for about 10 minutes while you prepare the other components.

Split the brioche burger buns and spread the cut sides with the softened unsalted butter.

Wash and pat dry the green leaf lettuce, slice the tomato into rounds, and thinly slice the red onion if not already prepared.

In a small bowl, stir together the mayonnaise, ketchup, and yellow mustard until smooth to make a simple burger sauce, then set aside.

Heat a large skillet or grill pan over medium-high heat and add the olive oil, swirling to coat the surface.

When the oil is hot and shimmering, place the brisket patties in the pan, indentation side up, leaving a little space between each one.

Cook the patties without moving them for about 4 to 5 minutes, until the bottoms are well browned and a crust has formed.

Flip the patties and cook for another 3 to 4 minutes for medium doneness, or until they reach your preferred internal temperature.

During the last minute of cooking, place a slice of cheddar cheese on each patty, cover the pan, and let the cheese melt.

While the cheese is melting, place the buttered brioche buns cut-side down in another skillet or on the edge of the pan to toast for 1 to 2 minutes, until golden.

Transfer the toasted bun bottoms to serving plates and spread each with about 1 tablespoon of the burger sauce.

Top each sauced bun bottom with a leaf of green lettuce, a slice or two of tomato, and a few slices of red onion.

Place a hot, cheesy brisket patty on top of the vegetables on each bun.

Spread a little of the remaining burger sauce on the cut side of the top buns if desired, then cap each burger and serve immediately while hot and juicy.