Lazy Lasagna Bolognese

INGREDIENTS

• 1/2 pound mushrooms
• 1 onion (1/2 lb.), peeled and chopped
• 2 tablespoons olive oil
• 1 cup finely chopped parsley
• 1 pound ground beef chuck
• 1/2 pound mild Italian sausages, casings removed
• 1/2 teaspoon dried thyme
• 2 tablespoons balsamic vinegar
• 1 can (6 oz.) tomato paste
• 1 can (8 oz.) tomato sauce
• 2 cups fat-skimmed chicken broth
• Béchamel Sauce
• 1 box (9 oz.) oven-ready dried lasagna
• About 1 1/4 cups shredded parmesan cheese (about 5 oz.)
• 1/4 teaspoon ground nutmeg