Prepare the pesto: place the basil, minced garlic, and pine nuts in a food processor or blender and pulse until coarsely chopped.
With the machine running, slowly stream in the 1/2 cup extra virgin olive oil until the mixture is smooth.
Add 1/2 cup freshly grated Parmesan-Reggiano and pulse until combined, then season the pesto with salt and freshly ground black pepper to taste; set aside.
Cook the gnocchi according to the package instructions, then drain thoroughly in a colander.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat until shimmering.
Add the drained gnocchi in a single layer and cook undisturbed until the bottoms are golden and crisp, about 3–4 minutes.
Turn the gnocchi and continue cooking, turning occasionally, until all sides are golden and crisp, about 3 more minutes.
Remove the skillet from the heat and stir in 1/4 to 1/3 cup of the prepared pesto to coat the gnocchi; reserve any remaining pesto for serving.
Serve the gnocchi warm and top with additional Parmesan cheese if desired.
