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, tomato paste and season with salt and pepper. Add lid and bring to a boil.
Once sauce starts to boil, reduce heat to simmer. Add tomato paste and 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 a bit, stir in the cream. Carefully pour sauce into the blender with cheese and basil, and blend until smooth.
Taste, adjust seasoning and serve with your favorite prepared pasta.