Heat the olive oil in a saucepan or just a wide, rimmed pan over low heat. Add minced garlic and minced sundried tomatoes to the oil and stir the ingredients around until you hear the garlic start to sizzle in the pan. Next, stir the tomato paste into the pan. Break the tomato paste up until it starts to soften and coat the garlic and sundried tomatoes.
Turn the heat up a little and pour vodka into the sauce. Stir the ingredients as the alcohol cooks off, and adjust the heat as necessary so you don’t burn any of the other ingredients. Cook the vodka for 1 or 2 minutes like this, then pour in the heavy cream. Season the sauce with salt, onion powder, crushed red pepper flakes, and fresh chopped basil.
Bring the sauce to a simmer. Once it’s simmering, transfer a couple of spoonfuls of sauce to a small dish. Stir xanthan gum into the dish to create a slurry, then return the mixture to the main pot of sauce. Reduce the heat, stir the ingredients, and allow the sauce to bubble until it reduces. Once you have a thickened vodka sauce, allow it to cool off of the stove before serving. Allow the sauce to cool completely before storing any leftovers in your refrigerator.