Heat the extra-virgin olive oil in a large skillet over medium-low heat. Add the peeled and gently smashed garlic cloves 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, which should take about 10 to 12 minutes. If the garlic starts to burn, reduce the heat to medium-low. Season the mixture with crushed red pepper flakes (if using), kosher salt, and freshly cracked black pepper. Then, reduce the heat to medium-low and stir in the heavy cream, letting everything come together into a creamy sauce. I always like to let the tomatoes cook slowly here—this deepens the flavor wonderfully.
While the sauce is cooking, bring a large pot of salted water to a boil. Add the potato gnocchi and cook according to the package instructions until al dente. Before draining, reserve 1/2 cup of the pasta cooking water, then drain the rest. I find that saving some pasta water always helps to create a silkier sauce when combining everything.
Transfer the cooked gnocchi and reserved pasta cooking water to the skillet with the tomato sauce (from Step 1). Toss everything together continuously over medium heat until the sauce is thickened and glossy, about 2 minutes. Stir in most of the fresh basil leaves, reserving a little for garnish at the end.
Break the fresh burrata balls into generous pieces and scatter them evenly over the creamy, sauced gnocchi. Remove the skillet from the heat and finish the dish by garnishing with the reserved fresh basil. For an extra fresh touch, I love to drizzle a bit more olive oil over the finished dish just before serving.