Roast the tomatoes. Preheat the oven to 425°F (220°C). To a tray, add the washed tomatoes, a pinch of salt, and the light olive oil. Mix them well. Roast in the oven until blistered and soft (about 20 minutes).
Make the pesto. While the tomatoes are roasting, make the pesto. Add the basil leaves, pine nuts, minced garlic, salt, and pepper to a food processor or blender and puree/blend for about 20 seconds. Then, add the grated parmesan and process it/blend it until everything is finely minced. While processing/blending, slowly add the olive oil. Adding it slowly while blending/processing it helps emulsify the pesto. Taste it and adjust it to your preference. For detailed step-by-step instructions, you can follow my separate pesto recipe.
Boil the gnocchi. Bring a pot of salted water (about 1 tbsp salt) to a boil. Once the water is boiling, add the gnocchi and cook according to package instructions. They’ll be ready when they float. For fresh homemade gnocchi, it can be as quick as 1 minute. For store-bought, it can take 2-3 minutes. As soon as they float, reserve 1 cup of water* and drain them. *Note. You’ll only need 1/3 cup of the water in the next step, but it’s best to reserve extra in case you want to adjust the sauce consistency.
Combine everything. In a pot over low heat, combine the pesto, freshly ground black pepper, lemon zest, 1/3 cup of gnocchi water, and the cooked gnocchi. Add the roasted tomatoes and gently combine.
Serve. Serve with freshly grated parmesan on top and any optional add-ons like burrata (mentioned in the ingredient notes).