Mushroom and Tomato Lasagna

Name: Mushroom and Tomato Lasagna
Ingredients: 10 plum tomatoes, halved lengthwise; 1/4 cup chopped flat-leaf parsley; 7 garlic cloves, minced; Salt and freshly ground pepper; 1/2 cup pure olive oil, plus more for the noodles; 1 1/4 pounds wild mushrooms, thinly sliced; 3 medium leeks, white and tender green parts, coarsely chopped; 1 stick (4 ounces) unsalted butter; 2/3 cup all-purpose flour; 1 quart milk, at room temperature; Pinch of freshly grated nutmeg; 1 pound dry lasagna noodles; 1/2 pound mild goat cheese, at room temperature; 2/3 cup fresh whole-milk ricotta (6 ounces); 2 tablespoons chopped basil; 1 large egg, beaten; 1 1/4 cups shredded mozzarella cheese, (4 ounces)