Bring a large pot of generously salted water to a boil.

Meanwhile, heat the olive oil in a medium skillet over medium low heat. Add the cherry tomatoes, a pinch of salt, and several grinds of pepper. Cook, stirring occasionally, for about 6 minutes, or until the tomatoes soften, burst, and release their juices. Remove the skillet from the heat.

Cook the gnocchi in the boiling water for 2 to 3 minutes, or until they float to the surface. Using a slotted spoon or spider strainer, transfer the cooked gnocchi directly from the pot to the skillet with the tomatoes. Reserve about 1 cup of the gnocchi cooking water.

Gently stir to combine the gnocchi and tomatoes. Add the pesto and stir gently until everything is evenly coated. If the sauce seems too thick, add the reserved pasta water, one tablespoon at a time, until it reaches a light, creamy consistency that coats the gnocchi.

Taste and season with more salt and pepper if needed. Divide into bowls and top with toasted pine nuts, fresh basil leaves, and a generous sprinkle of freshly grated Parmesan cheese. Serve immediately.