Prep the Burger Patties: In a large mixing bowl, combine the ground beef, egg, French onion soup mix, seasoning salt, and Worcestershire sauce. Mix until just combined, make sure not to over-mix because it will make the burgers dense and tough.
Make the Burger Patties: Divide the beef mixture into 5 equal portions and shape each portion into a round, flat patty, about 1/2-inch thick.
Grill the Patties: Preheat your grill to medium-high heat. Place the patties on the grill and cook for about 4 to 5 minutes on each side, or until the burgers are well browned and cooked to your desired level of doneness. Use a meat thermometer to ensure they reach an internal temperature of at least 160°F (71°C) for safety.
Add the Cheese: During the last minute of grilling, place a slice of cheese on each patty. Close the grill lid to help the cheese melt evenly.
Toast the Buns:Cut the brioche buns in half and lightly butter the cut sides if desired. Place them cut-side down on the grill during the last 2 minutes of cooking to lightly toast them.
Assemble the Burgers: Place each grilled cheese-topped patty on a toasted brioche bun bottom. Add optional toppings such as tomatoes, lettuce, pickles, and your desired condiments. Cover with the top half of the brioche bun.