French Onion Burger

Name: French Onion Burger
Ingredients: For the onions:; 3 tablespoons olive oil; 2 medium yellow or white onions, thinly sliced; For the sandwiches:; 1 tablespoon olive oil; 1 shallot, minced; 3 tablespoons dry vermouth or dry white wine; 1 1/4 pounds lean ground beef; 1 tablespoon coarse black pepper; 1/2 teaspoon salt; 4 Sara Lee Artesano Brioche Hamburger Buns; 4 tablespoons unsalted butter, softened; 1 teaspoon fresh thyme, finely chopped; 1/2 teaspoon Worcestershire sauce; 4 slices Gruyère cheese