Begin by bringing a large pot of salted water to a boil.
While the water heats up, warm olive oil in a large skillet over medium-low heat. Add garlic and cook for about 2 minutes until it becomes fragrant.
Increase the heat to medium, add tomatoes, and cook for 10-12 minutes until they break down and become jammy. Season with red pepper flakes (if using), salt, and black pepper.
Reduce heat to medium-low and stir in the heavy cream.
When the water boils, add gnocchi and cook according to the package instructions until al dente. Save 1/2 cup of pasta cooking water and drain the rest.
Transfer the cooked gnocchi and reserved pasta water to the skillet with the tomato sauce. Toss continuously until the sauce thickens and becomes glossy, about 2 minutes. Stir in fresh basil, saving some for garnish.
Break burrata balls into pieces and distribute evenly over the pasta. Remove the skillet from heat and garnish with reserved basil.