01 - Bring a large pot of salted water to a boil over high heat.
02 - In a food processor, combine basil, garlic, pine nuts, and Parmesan. Pulse until coarsely chopped. With the motor running, slowly stream in the olive oil until a smooth, creamy sauce forms. Season with salt, pepper, and lemon juice if using. Set aside.
03 - Add gnocchi to the boiling water and cook according to package instructions, usually until they float to the surface, approximately 2 to 3 minutes.
04 - Drain the gnocchi in a colander, reserving about 1/4 cup of the cooking water.
05 - Transfer hot gnocchi to a large bowl and toss with the prepared pesto. Add a splash of reserved cooking water if needed to achieve a silky, coating consistency.
06 - Plate immediately, topping with additional grated Parmesan, fresh basil leaves, and extra pine nuts if desired.