Preheat a large skillet over medium heat and add the olive oil.
Add the garlic and red pepper flakes; sauté gently for about 1 minute, until fragrant but not browned.
Add the cherry tomatoes and season with salt and pepper. Cook for 6 to 8 minutes, stirring occasionally, until the tomatoes blister and begin to break down into a chunky sauce.
Stir in the heavy cream, basil, and a generous amount of salt and black pepper. Cook for another 3 to 5 minutes, until the sauce thickens and develops a glossy texture.
Meanwhile, bring a large pot of salted water to a boil. Add the gnocchi and cook until they float to the surface and are tender, usually about 2 to 3 minutes. Scoop out and reserve a cup or two of the starchy pasta water.
Add the cooked gnocchi to the sauce and stir to combine. Add enough pasta water (1 to 2 cups) as needed, a little at a time, to create a creamy, glossy consistency that coats the gnocchi.
Remove the skillet from the heat and gently fold in the burrata, being careful not to break it apart. Let the burrata melt into the sauce slightly for about 1 minute.
Divide the creamy tomato gnocchi among four plates or bowls. Serve immediately, garnished with additional torn basil and a pinch of red pepper flakes, if desired.