NO-COOK TOMATO SAUCE

1(28-ounce) can crushed tomatoes
¼cup chopped fresh basil
2tablespoons extra-virgin olive oil
2 garlic cloves, minced
1teaspoon kosher salt
¼teaspoon red pepper flakes
NO-COOK CREAM SAUCE

4ounces Parmesan cheese, grated (2 cups)
1cup whole milk cottage cheese
1cup heavy cream
2 garlic cloves, minced
1teaspoon cornstarch
½teaspoon kosher salt
½teaspoon pepper
VEGETABLE FILLING

1 ½pounds eggplant, peeled and cut into ½-inch cubes (about 7 cups)
Kosher salt and ground black pepper
1pound zucchini, cut into ½-inch pieces (about 4 cups)
1pound yellow squash, cut into ½-inch pieces (about 4 cups)
5tablespoons plus 1 teaspoon extra virgin olive oil
4 garlic cloves, minced
1tablespoon minced fresh thyme
12ounces baby spinach (about 12 cups)
12 no-boil lasagna noodles
½cup minced pitted kalamata olives
12ounces low-moisture whole-milk mozzarella cheese, shredded (about 3 cups)
2tablespoons chopped fresh basil