Ingredients:

• 2 medium red onions, cut into 1/4″ slices
• 3 tablespoons butter
• salt and black pepper, sprinkling
• 2 tablespoon balsamic vinegar
• 2 cloves garlic, minced finely
• 1 cup half and half
• 1 tablespoon grainy mustard
• 2 cups Gruyere cheese, shredded
• 1/4 cup Parmesan cheese, freshly shredded
• 1 teaspoon paprika
• 3 tablespoons Worcestershire sauce
• hot sauce, a dash
• 1 1/2 – 2 lbs ground beef
• 4 hamburger rolls, halved

Directions:

1. Preheat the grill wiping the grates  and heating to a medium-high heat.
2. When the grill is hot, toss the onions slices with 2 tbsp. softened butter, balsamic vinegar, and a generous pinch of salt and black pepper in an sealed aluminum foil packet.  Place the onions on a medium part of the grill and grill until  the onions are tender, 15-20 minutes.
3. In a medium saucepan, combine the garlic, half and half, mustard, Gruyere, and Parmesan with a generous pinch of salt and the paprika. Stir to blend. Warm over low heat, whisking, until the cheese melts and the sauce become smooth (8-10 minutes). Stir in Worcestershire sauce and a splash of hot sauce. Taste and adjust seasonings as needed.
4. In a medium bowl, break up the meat and season generously with salt and add 1 tablespoon Worcestershire sauce. Mix with your hands to make sure all of the flavors get integrated. Form the meat into four even patties that are about 3/4-inch thick. Take care not to overwork the meat here.
5. Place the hamburgers on the hottest part of the grill and cook, undisturbed, for about 3-4 minutes. Turn them a quarter turn and cook for 2 more minutes. Use a metal spatula to flip them on their second side and cook for an additional 3-4 minutes for medium burgers. Toast the bun halves on the coolest part of the grill. Place a hamburger on the bottom bun and top with cheese sauce. Place onions on top and serve.