Bring a large pot of salted water to a boil. Add gnocchi and cook according to package directions until they float, about 2-3 minutes. Reserve 1/2 cup pasta water before draining.
Heat olive oil in a large skillet over medium heat. Add sliced garlic and cook until fragrant, about 90 seconds.
Add cherry tomatoes, salt, and black pepper. Cook for 12 minutes, stirring occasionally, until at least half the tomatoes burst and break down into a chunky sauce.
Stir in heavy cream and red pepper flakes if using. Add the cooked gnocchi and reserved pasta water. Toss for 2 minutes until sauce thickens and coats the gnocchi.
Remove from heat. Tear in most of the basil leaves. Break up burrata over the top and garnish with remaining basil. Serve immediately.