Bring a large pot of salted water to a boil. Meanwhile, heat the olive oil in a large skillet over medium-low heat. Add the garlic and cook until fragrant, about 2 minutes.

Increase the heat to medium and add the cherry tomatoes. Cook, stirring occasionally, until most of the tomatoes break down and become jammy, about 10 to 12 minutes. If the garlic starts to burn, reduce the heat to medium-low. Season with red pepper flakes (if using), salt, and black pepper. Reduce the heat to medium-low and stir in the heavy cream.

When the water boils, add the gnocchi and cook according to package directions until al dente. Reserve 1/2 cup of the pasta cooking water, then drain the gnocchi. Transfer the cooked gnocchi and reserved water to the skillet with the tomato sauce. Toss continuously until the sauce thickens and becomes glossy, about 2 minutes. Stir in most of the fresh basil, reserving some for garnish.

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