Boil the noodles to almost al dente, about 6 minutes. Strain the pasta from the water and set aside to cool.
In a skillet add the olive oil, carrot, onion and 1 teaspoon of salt. Cook for 5 minutes. Add 3 cloves of garlic to the skillet. Cook for 1 minute. Add white wine, cream and tomatoes. Simmer for 15 minutes.
While the sauce is simmering, combine the ricotta, mascarpone, parmesan cheese, ground beef, 1 teaspoon salt, 2 garlic cloves and basil in large bowl.
Pour half of the sauce into a heat proof bowl. Set aside.
Stuff the cooked shells with the ricotta beef mixture. Place the stuffed shells into the sauce. Spoon the remaining sauce over the stuffed pasta. If you prefer to cook the shells in a baking pan, add a layer of sauce to the bottom of the pan. Place the stuffed pasta into the pan and cover with the remaining tomato sauce.
Place into the oven and bake for 50 minutes. Top with freshly grated parmesan and freshly torn basil.
This pasta dish can be prepped 6-8 hours before baking. Remove from the refrigerator at least an hour before baking. If you would like to top with cheese before baking, a combination of shredded mozzarella and parmesan would work well.