In a food processor, pulse the parsley, cheese, pistachios, 4 tbsp. lemon juice and the garlic until finely chopped; season with salt and pepper. With the machine running, stream in the EVOO and process until a finely ground pesto forms.
In a medium saucepan, melt the butter over medium. Add the pasta and cook, stirring often, until toasted, about 2 minutes. Add the rice and scallion whites; season and cook until the scallions wilt, about 1 minute. Add the stock and bring to a boil. Cover and reduce the heat to low. Cook, shaking the pan occasionally, until the rice is just tender, 15 to 18 minutes. Using a fork, fluff the rice and mix in the scallion greens.
When the rice is almost done, season the fish. In a large nonstick skillet, heat the olive oil, two turns of the pan, over medium-high. Add the fish and cook until browned on both sides and almost opaque but still a bit pink at the center, about 6 minutes. Douse the fish with 2 tbsp. lemon juice.
Place the salmon on dinner plates and top liberally with the pesto. Serve the rice alongside.