Place a grill pan over medium-low heat or preheat a gas or charcoal grill.
Heat 2 tablespoons of the oil in an 8-inch nonstick skillet over medium-high heat. Add the shallots, 3/4 teaspoon salt and 1/4 teaspoon pepper. Cook until the shallots are soft, 3 minutes. Add the garlic and cook until aromatic, 30 seconds. Remove the pan from the heat and cool slightly.
Combine the shallot mixture, lamb, cumin, ketchup, 1/2 teaspoon salt and 1/4 teaspoon pepper in a medium bowl. Form the mixture into 8 patties each 2 1/2 inches in diameter and 1/2-inch thick. Press a cube of cheese into the middle of each patty and form the meat around the cheese to cover. Brush the patties with the remaining 3 tablespoons of oil and grill until cooked through, 5 to 6 minutes per side. Let the patties rest for 2 minutes. Place the patties in the buns and serve.