For the Caramelized Onions:
1 tablespoon olive oil
2 tablespoons butter
2 large onions, diced
1 large bay leaf
1 teaspoon ground thyme
Salt and fine black pepper or white pepper
½ cup beef bone broth or stock
For the Patty Melts:
4 large brioche burger rolls
1 ½ pounds ground sirloin, 80/20
1 tablespoon Worcestershire sauce
Salt and coarse black pepper
Non-aerosol cooking spray
Melted butter, for brushing
14 ounces Gruyere, to shred, or 12 slices from deli counter, if available
Thinly sliced cornichons
For the caramelized onions, heat olive oil over medium heat, add butter and melt. Add onions, bay leaf, thyme, salt and pepper and cook 15 minutes to soften. Add bone broth and cook 30 minutes more, stirring occasionally.
For the patty melts, halve the rolls and press to flatten. The patty melts are made with the cut sides facing out, resulting in a brioche grilled cheese with a thin beef patty in the middle.
Season beef with Worcestershire and salt and pepper, score meat to portion, then form 4 very thin patties.
Heat a large nonstick skillet or griddle over medium-high heat. Spray pan with cooking spray and cook patties until brown and crisp, 5 minutes on one side, then flip and cook 2 minutes more. Remove from pan.
Wipe pan clean and dry and return to stovetop.
To assemble patty melts, lightly brush cut sides of brioche with butter and build with cut sides out: add caramelized onions, cheese, patty, more cheese, a swirl of Dijon, sliced cornichon and inverted bun top.
Heat pan over medium. Griddle the patty melts until golden and cheese is melted.