Caramelize the Onions: In a large, heavy-bottomed skillet or Dutch oven, melt the butter with the olive oil over medium heat. Add the thinly sliced onions and cook for 10 minutes until soft and translucent. Reduce the heat to low and continue cooking, stirring occasionally to prevent burning, for another 25–30 minutes, or until the onions are deep golden brown and very soft.

Brown the Beef: Increase the heat to medium-high. Add the ground beef directly into the caramelized onions. Break the beef apart with a spoon and cook until fully browned and no pink remains. Drain any excess fat if necessary (leaving about 1 tbsp for flavor).

Build the Gravy: Sprinkle the all-purpose flour over the beef and onion mixture. Cook and stir for 1–2 minutes to toast the raw flour. Add the minced garlic, fresh thyme, salt, and black pepper, and cook for 30 seconds until fragrant.

Simmer the Filling: Slowly pour in the beef broth and Worcestershire sauce, stirring constantly to prevent lumps. Bring the mixture to a low boil, then reduce the heat and let it simmer uncovered for 10–15 minutes, or until the sauce has thickened and the flavors have melded. Adjust seasoning with salt and pepper.

Toast the Buns: While the filling simmers, split the brioche buns and toast them until lightly golden.

Assembly: When ready to serve, place the bottom half of each toasted brioche bun on a plate. Top generously with the hot French Onion Beef filling. Place a slice of Provolone cheese directly on the hot filling. Optional: Place under a broiler for 1 minute to melt the cheese perfectly.

Final Polish: Finish with the top half of the toasted brioche bun. Serve immediately, messy and glorious!