Bring a large pot of salted water to a boil. Add gnocchi and cook according to package directions, usually 2-3 minutes until they float to the surface. Reserve 1/4 cup pasta water, then drain.

Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the cooked gnocchi in a single layer and cook without stirring for 3-4 minutes until golden and crispy on the bottom. Flip and cook another 2 minutes.

Reduce heat to low. Add the pesto and reserved pasta water to the skillet. Toss gently to coat all the gnocchi evenly. If needed, add more pasta water to create a silky sauce.

If using cherry tomatoes, add them to the pan and toss for 1 minute until just warmed through.

Transfer the pesto gnocchi to a serving platter or individual plates. Tear the burrata into large pieces and arrange on top of the hot gnocchi.

Drizzle with remaining olive oil, sprinkle with red pepper flakes if desired, and garnish with fresh basil leaves and cracked black pepper. Serve immediately while hot.