Make the pistachio pesto: add pistachios, sun-dried tomatoes, garlic, basil, crushed red pepper (if using), and a pinch of black pepper to a food processor or blender and pulse until coarsely chopped.
With the motor running, stream in 2 tablespoons olive oil and process until smooth, then add 1/2 cup grated Parmesan and pulse until combined; season with salt and additional pepper to taste and set aside.
Cook the gnocchi according to package instructions; before draining, reserve 1 cup of the cooking water, then drain the gnocchi completely.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add gnocchi in a single layer (work in batches if needed) and cook undisturbed until the bottoms are golden and crisp, about 3–4 minutes.
Turn the gnocchi and continue to cook, turning occasionally, until all sides are golden and crisp, about 3 more minutes.
Remove the skillet from the heat, add the pistachio pesto and a splash of reserved cooking water as needed to loosen the sauce, then toss to coat the gnocchi evenly.
Serve warm and garnish with extra basil and grated Parmesan, if desired.
