In a large skillet over medium heat, melt the butter and olive oil. Add the onion and cook for 6 minutes, stirring occasionally, until slightly softened. Add the garlic and cook for one more minute.

Add the tomato paste to the skillet and stir well to combine. Let cook for 2 to 3 minutes, stirring frequently, until it has darkened in color.

Pour in the vodka. Using a wooden spoon, scrape up any brown bits from the bottom of the pan. Let the mixture simmer for about 3 minutes, stirring frequently, until the vodka has almost fully reduced.

Add the canned tomatoes and the salt. Using the wooden spoon, break each of the tomatoes in half. Let the mixture simmer, stirring occasionally, for about 10 minutes, until it’s slightly reduced. Remove from the heat.

Carefully ladle the mixture into the canister of a blender. Place the lid on the canister, but remove the center insert to leave an vent. Hold a paper towel or clean dish towel loosely over the opening. Puree on medium-low speed until almost smooth, about 30 seconds. Pour the mixture back into the skillet. (You can also use an immersion blender.)

If serving with pasta, bring a large pot of salted water to a boil over high heat. Add the pasta and cook it according to the package instructions. Reserve 1 cup of pasta water and drain the pasta in a colander.

If adding pasta, stir it in along with ¼ cup of the reserved pasta water until the pasta is well coated. (If the sauce is too thick, add more of the reserved pasta water 1 tablespoon at a time, to reach your desired consistency). Serve immediately, topped with more freshly grated parmesan cheese and basil if desired.

The pasta sauce can be refrigerated in an airtight container for up to 5 days.