Bring a large pot of salted water to a rolling boil.
While waiting, warm the olive oil in a large skillet over medium-low heat and gently sauté the garlic until it releases its aroma, about 2 minutes.
Turn the heat up to medium, add the cherry tomatoes, and cook them down, occasionally stirring, until they soften and become jam-like, roughly 10 to 12 minutes. Lower the heat if garlic begins to brown. Season the mixture with red pepper flakes if you like a bit of heat, salt, and black pepper.
Turn the heat down to medium-low and blend in the heavy cream until fully combined.
Once the water is boiling, add the gnocchi and cook per the package directions until tender but still firm. Scoop out half a cup of the cooking water before draining the gnocchi.
Add the cooked gnocchi and reserved pasta water into the skillet with the tomato sauce. Stir and toss continuously until the sauce thickens and coats the gnocchi with a glossy finish, about 2 minutes. Mix in most of the fresh basil, keeping some aside for decorating.
Tear the burrata cheese into chunks and scatter it over the gnocchi. Remove the skillet from the heat and sprinkle with the remaining basil for a fresh touch.
