Combine butter and cheese in dish, and reserve.
Combine meat, sage, garlic and lemon zest; season with salt and pepper. Form four patties and drizzle with oil. Cook on griddle pan or in a large skillet over medium-high heat for 10-12 minutes, turning occasionally.Remove to plate. Add ham to skillet and crisp on both sides, about 2 minutes, turning occasionally.
While burgers cook, char rolls under a broiler then slather with gorgonzola butter while hot.
Serve burgers on rolls topped with crispy ham. If using spinach, wilt up a bit and stack onrolls under patties.