Soak wooden skewers in water for at least 10 minutes.
Meanwhile, make the pesto and preheat a grill to high.
For the pesto, pulse walnuts, lemon zest, lemon juice, olive oil, garlic olive oil and a pinch of salt in a food processor until the walnuts are in small pieces. Pulse in the scallions, basil, parsley until fairly smooth – with machine on, drizzle in 2-3 tablespoons of cold water to loosen if necessary. Transfer to bowl and season with salt, to taste.
Divide the pesto into two bowls. Set one aside.
Thread the shrimp onto the pre-soaked skewers, brush shrimp with pesto from one bowl, making sure to brush both sides of the shrimp. Discard remaining pesto from bowl used to brush shrimp.
Add shrimp to the grill and cook just a couple minutes per side until they’re pink and opaque. Remove from the grill and brush with a little of the remaining pesto, serving the rest on the side.
Serve over mixed greens or rice.