Mix cheese and cornstarch together in a small bowl. Rub garlic all over the inside of a medium saucepan, add the clove and lager to the saucepan and bring to a gentle boil. Add handfuls of cheese to the saucepan, stirring in between handfuls, until melted, and bring to a boil. Add mustard, salt and pepper and simmer over moderate heat until sauce begins to thicken, about 2 minutes; keep warm over very low heat.
Lightly knead the sirloin and the chuck together in a bowl. Form 4 large equal patties about 3/4 thick. Season the burgers generously with salt and pepper and put on a saran wrap covered plate. Brush the insides of the buns with the melted butter.
Light your grill and oil the grate once it is heated. Grill the burgers for about 10 minutes, turning once, for medium. Remove the burgers from the heat source and lightly grill insides of the buns until just toasted.
Place a lettuce leaf and tomato slice on the bottom of each bun. Top each with a burger and a generous helpings of cheese sauce. Cover with bun and serve, passing the remaining cheese sauce to serve on the side.