Melt 2 tablespoons butter in a skillet over low heat; add onions. Simmer 30-45 minutes to caramelize and develop a deep golden color, adding small amounts of water as necessary to prevent burning. Add brandy, simmer and stir until alcohol has cooked off and the flavors combine, 3-5 minutes; set onions aside and keep warm.
In a medium mixing bowl, hand blend thyme and shallots with the ground beef, form into four patties and season both sides with salt and pepper. Refrigerate 10-15 minutes.
Brush cut sides of buns with butter and pan sear or grill to golden brown.
Pan sear or grill patties 4-5 minutes on one side, flip and top each with caramelized onions and Gruyère cheese. Continue to cook another 4-5 minutes until the burger reaches an internal temperature of 160°F.
Spread Dijon on bottom half of buns, top with burgers and bun tops.
