1. Cook pasta according to package directions, omitting salt and fat. Drain; keep warm.
2. While pasta cooks, combine milk, 2 teaspoons basil, salt, and pepper in a bowl; stir milk mixture with a whisk.
3. Heat a small saucepan over medium heat. Add oil to pan; swirl to coat. Add flour to pan, and cook for 2 minutes, stirring constantly. Add milk mixture; cook for 3 minutes or until slightly thickened, stirring frequently. Remove from heat, and add 1 1/2 ounces Parmigiano-Reggiano and mascarpone cheese to milk mixture. Add cheese mixture to pasta; toss to combine. Sprinkle with remaining 4 teaspoons basil and remaining 1/2 ounce Parmigiano-Reggiano.