Butternut Squash and Mushroom Lasagna

Name: Butternut Squash and Mushroom Lasagna
Cuisine: European, Italian, Mediterranean
Ingredients: 1/4 cup (1/2 stick) unsalted butter; 2 1/2 cups chopped onions; 1/2 pound crimini (baby bella) mushrooms, sliced (about 3 cups); 2 pounds butternut squash, peeled, seeded, cut into 1/4-inch-thick slices (about 5 1/2 cups); 1 14-ounce can vegetable broth; 4 tablespoons chopped fresh thyme, divided; 4 tablespoons sliced fresh sage, divided; 3 15-ounce containers whole-milk ricotta cheese; 4 cups grated mozzarella cheese, divided; 2 cups grated Parmesan cheese, divided; 4 large eggs; Olive oil; 1 9-ounce package no-boil lasagna noodles