Heat the olive oil in your large deep skillet over medium heat. Add the diced onion and cook until translucent and slightly golden, about 4-5 minutes.
Toss in the minced garlic and sauté for another 1 minute until fragrant, careful not to burn it.
Add the Calabrian chili paste to the skillet and stir well to combine with the onion and garlic. Let it cook for about 1-2 minutes to release its smoky, spicy flavor.
Pour in the chicken broth, heavy cream, and diced tomatoes. Stir everything together, scraping the bottom of the pan to deglaze and mix the flavors.
Add the penne pasta directly to the sauce, making sure the pasta is submerged.
Bring the mixture to a gentle boil, then reduce the heat to medium-low. Cover and let it simmer, stirring occasionally, until the pasta is al dente and the sauce has thickened, about 12-15 minutes. Add a splash of water or broth if the sauce gets too thick before the pasta is fully cooked.
Once the pasta is tender and the sauce is creamy, season with salt and black pepper to your liking.
Remove the pan from heat and stir in the grated Parmesan cheese until melted and smooth.
Serve your One-Pot Spicy Vodka Pasta hot, garnished generously with fresh basil leaves.