Prepare the Tangy Remoulade: In a medium bowl, whisk together mayonnaise, Dijon mustard, ketchup, dill pickle relish, finely chopped capers, Worcestershire sauce, lemon juice, paprika, and chopped fresh parsley. Cover and refrigerate for at least 30 minutes to allow flavors to meld.

Season the Beef: In a large bowl, gently combine the ground beef with Worcestershire sauce, soy sauce, garlic powder, onion powder, black pepper, and salt. Avoid overmixing to maintain tenderness. Divide the mixture into six equal portions and form into patties about 3/4 inch thick, creating a slight indentation in the center of each patty to prevent puffing up during cooking.

Cook the Patties: Heat a grill or a cast-iron skillet over medium-high heat. Cook the patties for approximately 4-5 minutes per side for medium doneness, or adjust time for your preferred level of cook. Avoid pressing down on the patties while they cook to retain juices.

Melt the Cheese: During the last minute of cooking, place a slice of Provolone cheese on top of each patty. If using a skillet, you can cover it briefly to encourage melting.

Toast the Buns: While the cheese melts, lightly butter the cut sides of the brioche buns. Toast them on the grill or in a separate pan until golden brown.

Assemble the Burgers: Spread a generous amount of the prepared remoulade sauce on both halves of the toasted buns. Place a beef patty with melted cheese on the bottom bun, followed by lettuce leaves and tomato slices. Top with the other half of the bun.