Bring a large pot of water to boil. Once boiling, add the rigatoni and plenty of salt (about 1 tablespoon) and cook until al dente. Reserve 1 cup of pasta water and set aside.
Meanwhile, heat the butter and olive oil in a large, deep pot set over medium heat. Add the shallots, garlic, and red pepper flakes. Cook, stirring, until they begin to soften and turn translucent, 3 to 4 minutes.
Pour in the white wine and cook, stirring, until reduced by half, about 4 minutes. Whisk in the ricotta, lemon zest, and lemon juice until very well combined and the mixture comes to a gentle simmer. Remove from the heat.
Add the pasta to the sauce and toss until it is well-coated. Add 1 teaspoon salt, freshly ground black pepper, and grated Parmigiano-Reggiano. Stir to combine. Your sauce should feel a little too thick right now, even though it is coating the pasta. Add 1/4 cup of pasta water at a time, stirring, until the pasta sauce is glossy and reaches your desired consistency. I typically only use 1/4 cup of the reserved pasta water to achieve this.
Taste and add more salt and pepper, if desired. Stir in the basil until it just wilts. Garnish with more basil, a sprinkle of Parmigiano-Reggiano, and a few cracks of black pepper.