Boil water in a large pot to cook gnocchi. Place gnocchi in the pot. The gnocchi is done when they float to the top. Drain pasta and reserve 1/4 c. cooking water.
Puree half the tomatoes in a blender until smooth. Coarsely chop the remaining tomatoes, removing seeds and cores. Place pureed and chopped tomatoes in a liquid measuring cup and add reserved tomato liquid to equal 2 cups.
Heat oil in a saucepan over medium heat until it simmers. Add onion and tomato paste. Cook for about 3 minutes, stirring occasionally, until the onions are translucent.
Add garlic and red pepper flakes. Cook for about 30 seconds while stirring constantly.
Add tomatoes and 1/2 tsp. salt.
Remove the pan from the burner to add the vodka. Return pan to medium-high heat and simmer for approximately 8-10 minutes, stirring frequently until the alcohol flavor has cooked off. Lower the heat if the sauce simmers too vigorously.
Stir in heavy cream and cook for about 1 minute, until it is heated through.
Add sliced sausage, basil, 3 tbsp. parsley, and garlic butter to the sauce.
Simmer the sauce until the sausage is cooked through. 
Add cooked gnocchi to the sauce and simmer for an additional 30 seconds. Toss gnocchi to coat with sauce.  Add reserved pasta water if the sauce is too thick.
Serve gnocchi with Asiago cheese and remaining fresh chopped parsley as garnish.