Fill a large soup pot three-quarters full with water and bring to a boil over high heat. Add 4 tablespoons of salt and stir. Once the water is boiling, add the pasta and cook according to the package instructions until al dente. Drain, reserving ½ cup of the pasta cooking liquid, and set it aside.
In a Dutch oven or heavy-bottomed pan, heat 2 tablespoons of oil over medium heat. Add the shallot and sauté for 5 to 6 minutes, until softened. Stir in the garlic and cook for about 30 seconds, making sure it doesn’t burn. Add the Calabrian chili peppers and sauté for another 20 to 30 seconds. Stir in the tomato paste and cook for 3 to 4 minutes, stirring frequently.
Pour in the vodka to deglaze the pan, scraping up any bits from the bottom, then reduce the heat to low. Add the mascarpone and cream, stirring constantly until the sauce becomes smooth.
Using a slotted spoon, transfer the pasta into the sauce. Add ½ cup of the reserved pasta cooking liquid and stir to combine. Gradually add ¼ cup of Parmesan, stirring constantly to melt the cheese. Season with salt, and if needed, add a splash more pasta water to thin the sauce to your desired consistency.
Finish by topping the pasta with the remaining Parmesan, a drizzle of olive oil, and fresh basil. Enjoy!