Add the olive oil and onion into a deep skillet over medium-high heat and sauté for 5-7 minutes (ok if the onion lightly browns).
Add the garlic to the pan and cook for about 30 seconds.
Add the tomatoes and vodka and let it simmer for about a minute.
Stir in the Italian seasoning, half-and-half, and gnocchi. Give it a good stir, then reduce the heat to medium. Cover the pan and cook for 5 minutes.
Stir in the parmesan and basil. Season with salt & pepper as needed (I was fairly generous with the salt in this recipe) and cook for a couple more minutes to ensure the gnocchi is fully cooked through. Serve immediately.
The gnocchi will cook right in the sauce - no need to pre-cook it.