Heat the oil in a large skillet over medium heat. Add sliced garlic and cook for 2 minutes until fragrant but not browned.
Add the tomatoes and red pepper flakes. Cook for 5 minutes, then gently press tomatoes with a wooden spoon to burst them.
Season with salt and pepper, then simmer for 8-10 minutes until tomatoes break down completely into a chunky sauce.
Boil the gnocchi in salted water according to package directions (2-3 minutes). Reserve 1/2 cup pasta water before draining.
Stir in heavy cream to the tomato sauce and mix until silky and combined.
Add cooked gnocchi to the skillet with a splash of reserved pasta water. Toss gently to coat everything in sauce.
Fold in torn basil leaves, then turn off heat. Tear burrata into chunks and place on top. Let sit for 1 minute to soften.
Serve immediately with fresh basil and optional Parmesan cheese.
