1 tablespoon olive oil
1 (1 1/2 to 2-pound) butternut squash, peeled, seeded, and cut into 1-inch cubes
Salt and freshly ground black pepper
1/2 cup water
3 amaretti cookies, crumbled
1/4 cup butter
1/4 cup all-purpose flour
3 1/2 cups whole milk
Pinch nutmeg
3/4 cup (lightly packed) fresh basil leaves
12 no-boil lasagna noodles
2 1/2 cups shredded whole-milk mozzarella cheese
1/3 cup grated Parmesan