Filling
3 tablespoons plus 2 teaspoons olive oil
2 1/2 pounds (about 10) portobello mushrooms, stems trimmed
1 cup chopped prosciutto (about 6 ounces)
2/3 cup chopped shallots (about 2 large)
1 teaspoon chopped fresh rosemary
1 teaspoon chopped fresh thyme


Sauce
4 cups whole milk
1 14-ounce can low-salt chicken broth
1 bay leaf
1/2 cup (1 stick) butter
2/3 cup all purpose flour
2 cups (about 8 ounces) shredded Gruyère cheese
1/3 cup grated Parmesan cheese
1/8 teaspoon ground nutmeg


Lasagna
1 pound lasagna noodles
1/2 cup grated Parmesan cheese
2 tablespoons butter, cut into 1/2-inch pieces