Preheat oven to 350 degrees Fahrenheit (177 C). Bring 4 quarts water to boil in large pot over high heat.
Add 1 tablespoon extra-virgin olive oil, then add rigatoni. Cook until al dente, about 5 minutes. Drain rigatoni well in colander, shaking off excess water as they drain. Set aside.
In small saucepan, bring 2 cups whole milk, 3 tablespoons olive oil, 6 cloves garlic, 1/2 teaspoon kosher salt, 1/2 teaspoon freshly ground black pepper, and crushed red pepper to simmering point. Remove from heat and let stand 10 minutes.
Whisk vigorously until mixture thickens slightly.
Stir in remaining 1 cup whole milk and cook over medium heat until heated through, stirring frequently, about 8 minutes.
Season to taste with additional salt and pepper if necessary.
When ready to serve, toss rigatoni with creamy cheese sauce, dividing evenly between bowls. Serve immediately.