Bring a large pot of salted water to a boil. Cook the gluten free penne according to package directions until just al dente. Reserve 1/2 cup of pasta water before draining.
While the pasta cooks, heat the olive oil in a large deep skillet over medium heat. Add the minced garlic and red pepper flakes and cook for about 1 minute until fragrant.
Carefully pour in the vodka. Let it simmer for 2 to 3 minutes, stirring occasionally, until the liquid has reduced by about half and the raw alcohol smell has cooked off.
Add the crushed tomatoes, salt, and pepper. Stir to combine and let the sauce simmer gently for 10 minutes, stirring occasionally, until it has thickened slightly.
Reduce the heat to low and stir in the heavy cream until the sauce turns a uniform creamy pink color. Simmer for another 2 to 3 minutes.
Add the drained penne and parmesan cheese to the skillet. Toss everything together until the pasta is fully coated, adding a splash of reserved pasta water if the sauce needs loosening.
Serve in warm bowls topped with extra parmesan and torn fresh basil.