3 tbsp Unsalted butter
1 tbsp Red wine vinegar
2 Large cloves garlic (minced)
1/2 cup Whole milk
1/2 cup Heavy cream
1 tbsp Grainy mustard
2 cups Grated gruyere cheese
1/4 cup Finely grated Parmesan cheese
1 tsp Paprika
1 1/2 lbs Ground beef (preferably chuck and not too lean)
4 Seeded hamburger rolls (halved)
1 Small Serrano chili (cut into very fine slices)
Preheat the grill.
Prepare the onions: When the grill is hot, toss the onions slices with 2 tbsp. softened butter and a generous pinch of salt. Place them on a medium to low-heat part of the grill to char slowly. When the onions are tender, 12-15 minutes, remove them from the grill and toss them with the red wine vinegar. Set aside.
Make the cheese sauce: In a medium saucepan, combine the garlic, milk, cream, 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 a splash of Worcestershire and a splash of hot sauce. Taste for seasoning.
Make the hamburgers: In a medium bowl, break up the meat and spread it up on the sides so that the seasoning really permeates the meat. Season generously with salt and add 1 tbsp. Worcestershire. 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. It can toughen the texture of your burger!
Cook and assemble the burgers: 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 2-3 minutes for rare to medium-rare. Toast the bun halves on the coolest part of the grill. Place a hamburger on the bottom bun and top with grilled onions and Serrano chili slices. Pour some of the cheese sauce over the meat. Top with a bun and devour!