Prepare the sauce: Bring a large pot of salted water to boil. Heat olive oil in a large skillet over medium-low heat. Add sliced garlic and cook gently until fragrant and just beginning to turn golden, 2 to 3 minutes.
Cook tomatoes: Increase heat to medium and add cherry tomatoes. Cook, stirring occasionally, until tomatoes burst and break down into chunky sauce, 10 to 12 minutes. Use a wooden spoon to gently crush stubborn tomatoes.
Add cream: Season with salt, black pepper, and red pepper flakes if using. Reduce heat to medium-low and stir in heavy cream. Let simmer gently while cooking gnocchi.
Cook gnocchi: Add gnocchi to boiling water and cook according to package directions, 2 to 3 minutes, until they float. Reserve 1/2 cup pasta water before draining.
Combine: Add drained gnocchi and reserved pasta water to skillet with sauce. Toss continuously over medium heat for 2 minutes until sauce thickens and becomes glossy. Stir in half the basil.
Finish: Remove from heat. Tear burrata into large pieces and distribute over gnocchi. Garnish with remaining basil. Serve immediately.
