Prepare all ingredients.
In a 4-quart saucepan or Dutch oven, melt butter over medium heat. Add chopped onion and season with 1/2 tsp salt. Cook until onions soften (about 7 mins); then add sliced garlic and cook until onions turn translucent but not browned (2-3 mins).
Stir in tomato paste until thickened (3-4 mins), followed by crushed tomatoes. Combine well, let it thicken while stirring often (about 10 mins).
Pour in heavy cream. For a chunky sauce, stir gently. For a smooth sauce, use an immersion blender to puree.
Mix in Parmesan cheese; then reduce heat to medium-low. Add vodka and bring the sauce to a low simmer, cooking for 15 mins while stirring frequently.
Reserve half of the sauce for later use. Store in an airtight container in the fridge or freezer.
Combine beans with remaining sauce, gently stirring and letting it simmer for 2-3 minutes.
Serve with drizzled olive oil and balsamic vinegar, topped with extra Parmesan cheese, a sprinkle of chili flakes, and chopped parsley.
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