1. Heat oil in a large skillet over medium heat. Add lamb, working in batches if necessary, and cook, turning occasionally, until browned on all sides, 8 to 10 minutes. Return lamb to skillet and add pureed tomatoes, garlic, vinegar, and sugar; season with salt and pepper. Cover and simmer for 1 hour.

2. Meanwhile, melt butter in a medium nonstick skillet. Add orzo and cook, stirring constantly, until lightly golden, about 5 minutes. Transfer orzo to a large baking dish or six individual sized baking dishes.

3. Preheat oven to 350 degrees.

4. Transfer lamb mixture to baking dish or dishes with orzo. Carefully add hot water to dish and cover with parchment paper-lined aluminum foil. Place baking dish on a rimmed baking sheet and transfer to oven; bake for 1 1/2 hours.

5. Remove baking dish from oven and top lamb with tomato slices and cheese; season with salt and pepper. Return to oven and bake, uncovered, adding a little more water if necessary, until liquid is almost completely absorbed and pasta is al dente, about 30 minutes. Serve immediately with more cheese, if desired.