Bring a pot of water to boil. Add gnocchi and cook until floating, 5 to 6 minutes. Drain, reserving 1/2 cup cooking water.
Meanwhile, heat olive oil in a large pan over medium-low heat; add shallot and garlic. Gently cook until shallot has softened and garlic is fragrant, 3 to 5 minutes.
Turn heat up to medium and add the ground sirloin, salt, and red pepper flakes. Add in tomato paste. Allow tomato paste to caramelize. Pour in vodka and deglaze the pan by bringing sauce to a boil while scraping the browned bits with a wooden spoon. Let simmer for 5 minutes.
Pour cream into the pan and stir until the paste has completely incorporated. Allow to gently simmer until the sauce begins to thicken, 5 to 10 minutes. Sprinkle in 1/2 cup plus 2 tablespoons Parmesan cheese and stir until it melts.
Add drained gnocchi to the pan along with reserved 1/2 cup water. Serve topped with basil leaves.