Pre-heat the oven to 400°F.
On a baking sheet, arrange the tomato slices in a single layer and drizzle with EVOO; season with salt, pepper and the sugar. Roast for 30 minutes.
While the tomatoes are roasting, in a large nonstick skillet, cook the pancetta and onion over medium heat until browned, about 5 minutes. Transfer to a bowl to cool; wipe out the skillet and reserve. Add the beef, garlic and parsley to the pancetta mixture; season with salt and pepper. Form into four 3 1/2-inch-wide patties. When the tomatoes come out of the oven, pre-heat the broiler, arrange the split rolls cut-side up on a baking sheet and toast.
Heat 1 tablespoon EVOO, one turn of the pan, in the reserved skillet over medium-high heat. Add the beef patties and cook until browned and crisp on the bottoms, about 5 minutes, then flip and cook for 3 minutes more for medium-rare doneness.
In a small bowl, microwave the butter until melted, about 20 seconds. Brush the butter on the toasted rolls and top with the cheese. Broil for 1 minute.
Top each roll bottom with lettuce, a beef patty, tomatoes and a roll top.