Prepare Pasta Water and Ingredients: Bring a large pot filled with heavily salted water to a rolling boil. While waiting, finely chop the onion and mince the garlic cloves. Grate the Parmesan cheese if using a block.
Sauté Aromatics: Heat the olive oil in a deep skillet over medium-high heat until shimmering. Add the chopped onion and minced garlic and cook, stirring occasionally, until they become translucent and just start to turn golden, about 4 minutes.
Toast Tomato Paste and Spices: Stir in the tomato paste and red pepper flakes. Cook the mixture, stirring frequently, until the paste darkens slightly and releases a rich aroma, about 2 minutes. This step intensifies the sauce’s flavor.
Add Tomatoes and Vodka: Pour in the whole peeled tomatoes with their juices and the vodka. Use a wooden spoon or potato masher to break down the tomatoes into smaller chunks. Stir in the kosher salt, then bring the sauce to a gentle simmer.
Simmer Sauce to Thicken: Reduce heat to medium-low and let the sauce cook uncovered for about 15 minutes, stirring occasionally. This allows the flavors to meld and the sauce to thicken.
Cook Pasta Al Dente: Add the penne pasta to the boiling water and cook according to package instructions (usually 9-11 minutes) until just tender but still firm. Reserve one cup of pasta water before draining the pasta.
Blend Sauce Until Smooth: Transfer the sauce to a blender and blend for 30 seconds to 1 minute until smooth and creamy. Alternatively, use an immersion blender directly in the skillet. After blending, stir in the heavy cream with several short pulses or gentle stirring until combined.
Combine Pasta and Sauce: Return the sauce to the skillet over medium-high heat. Add the cooked penne, grated Parmesan, and 1/2 cup of the reserved pasta water. Toss constantly for about 4 minutes to evenly coat the pasta, adding more pasta water a tablespoon at a time if the sauce seems too thick.
Final Seasoning and Garnish: Turn off the heat and taste the pasta. Adjust seasoning with extra kosher salt and freshly ground black pepper if needed. Serve topped with sliced fresh basil, additional grated Parmesan, and a sprinkle of red pepper flakes for a little heat if desired.