Heat olive oil in a large skillet over medium-high heat. Pro tip: use a skillet with a lid.
Once oil is heated, add diced onion and cook until translucent, about 7–10 minutes. Add garlic and cook for another 1–2 minutes.
Add whole tomatoes and break up with the back of a wooden spoon. Pour in vodka and tomato paste, and season with salt and pepper. Cover and bring to a boil.
Once sauce starts to boil, reduce heat to simmer. Add balsamic vinegar. Cover and continue to simmer for about 20 minutes, stirring occasionally.
In a blender, grate parmesan cheese and add fresh basil leaves.
Once sauce has cooked and thickened, stir in the cream. Carefully pour sauce into the blender with cheese and basil, and blend until smooth.
Return sauce to the skillet and toss with your favorite prepared pasta, or spoon over pasta and serve immediately.