| 3 tablespoons extra virgin olive oil |
| 6 medium sweet potatoes, washed |
| 1 small butternut squash, halved, seeded |
| 1 small sugar pumpkin, halved, seeded |
| 1/2 cup pitted kalamata olives |
| 1/2 teaspoon minced fresh rosemary leaves |
| 6 tablespoons unsalted butter, room temperature |
Twelve 6-inch-square fresh lasagna noodles, or 12 extra-wide dry lasagna noodles
|
| Freshly grated Parmigiano-Reggiano cheese |