Bring a large pot of salted water to a boil.

Heat olive oil in a large skillet over medium-low heat.

Add garlic and cook until fragrant, about 2 minutes.

Increase heat to medium and add cherry tomatoes. Cook, stirring occasionally, until most of the tomatoes break down and become jammy, about 10 to 12 minutes. Reduce heat if garlic starts to burn.

Season the mixture with red pepper flakes (if using), salt, and black pepper.

Reduce heat again to medium-low and stir in the heavy cream.

When the water comes to a boil, add gnocchi and cook according to package instructions until al dente.

Reserve 1/2 cup of the pasta cooking water and drain the remaining water.

Transfer the cooked gnocchi and reserved pasta water to the skillet with the tomato sauce. Toss continuously until the sauce is thickened and glossy, about 2 minutes.

Stir in the fresh basil, reserving some for garnish.

Break the burrata balls into pieces and disperse them evenly over the pasta. Remove the skillet from heat and garnish with the reserved basil.