Begin by melting the butter in a large skillet over medium heat. Once melted, stir in the finely chopped shallot and garlic. Cook for 4 to 5 minutes, stirring often, until the mixture becomes soft and aromatic.

Add the tomato paste and crushed red pepper flakes to the pan. Stir well to coat the shallot and garlic, cooking for an additional 5 minutes or until the tomato paste turns a deeper, brick-red hue and begins to caramelize slightly.

Pour in the vodka and deglaze the pan, scraping up any bits stuck to the bottom. Stir until fully combined, then remove the skillet from heat and set aside.

In the meantime, bring a large pot of salted water to a rolling boil. Cook the pasta according to package instructions until al dente, stirring occasionally to prevent sticking. Before draining, reserve 2 cups of the starchy pasta water.

Return the skillet with the sauce to medium heat. Stir in the heavy cream and about ¼ cup of the reserved pasta water, mixing until the sauce is smooth and slightly thickened. Add half of the grated Parmesan and stir until fully melted and integrated into the sauce.

Remove the skillet from the heat and fold in the cooked pasta. Add the remaining Parmesan, mixing gently. If the sauce seems too thick or dry, gradually add more reserved pasta water, one tablespoon at a time, until the desired consistency is reached. Taste and adjust seasoning with kosher salt as needed.

Divide the pasta evenly among serving bowls. Finish each portion with an extra sprinkle of Parmesan and a few torn basil leaves for a fresh, fragrant touch. Serve warm.