Summer Garden Lasagna

Name: Summer Garden Lasagna
Ingredients: 1 teaspoon olive oil; 1 (16 ounce) package lasagna noodles; 3 ears corn, shucked; 1 tablespoon extra-virgin olive oil, divided; 2 zucchini, sliced into long ribbons using a vegetable peeler, discarding the seedy core; salt and ground black pepper to taste; 1/4 cup chopped onion; 1 clove garlic; 1 (24 ounce) jar marinara sauce, divided; 2 tablespoons heavy whipping cream; 2 cups ricotta cheese; 1 (9 ounce) package frozen chopped spinach, thawed and drained; 1 cup shredded mozzarella cheese; 1/4 cup grated Parmigiano-Reggiano cheese