Heat the oven to 375°F. Cook shells in water with the tablespoon salt until 2 minutes short of the package time, then drain gently and separate on a plate.
Heat oil in a skillet and cook mushrooms for 7 to 8 minutes until their water evaporates. Add beef and brown for 7 to 8 minutes until it reaches 160°F; drain excess fat and stir in garlic for 30 seconds.
Cool the beef mixture for 5 minutes, then mix with ricotta, 1/2 teaspoon filling salt and pepper. Meanwhile, melt butter in a saucepan, whisk in flour for 1 minute, then gradually whisk in milk and cream.
Simmer sauce for 3 to 4 minutes until lightly thickened. Remove from heat and stir in Parmesan and remaining salt; spread 1/2 cup sauce in a 9-by-13-inch baking dish.
Fill shells evenly with the beef mixture and arrange in the dish. Spoon remaining sauce over and between them, cover and bake for 25 minutes, then uncover for 5 to 8 minutes until the centers reach 165°F. Rest for 5 minutes before serving.