Cook the pasta according to the package instructions until al dente. Reserve about 1/2 cup of pasta water and then drain the pasta.
In a large skillet, melt 1 tablespoon of butter over medium heat. Add the diced shallot and minced garlic, and sauté until softened.
Add the tomato paste, Gochujang paste, and red pepper flakes to the skillet. Stir to combine and cook for 1-2 minutes.
Pour in the vodka and let it simmer for a couple of minutes, allowing the alcohol to cook off.
Reduce the heat to low and add the heavy cream, stirring continuously. Once the mixture is well combined, add the remaining tablespoon of butter and grated Parmesan cheese. Stir until the sauce is smooth and creamy.
Season the sauce with salt and pepper to taste. If the sauce is too thick, you can add a bit of the reserved pasta water to reach your desired consistency.
Add the cooked pasta to the skillet, tossing to coat the pasta evenly with the sauce.
Serve the pasta hot, garnished with additional Parmesan cheese if desired.