In a small skillet over medium heat, toast the walnuts, stirring occasionally, until fragrant and a shade darker, about 5 minutes. Let cool slightly on a plate, about 3 minutes, and then transfer to a food processor. Add the arugula, basil, Parmigiano, and garlic and process until the mixture is very finely chopped, about 1 minute. With the motor running, slowly add 4 Tbs. of the oil until well combined. If you like, add 1 Tbs. water to thin the pesto. Transfer to a bowl and season to taste with salt.
Heat a lightly oiled grill pan over medium-high heat. Rub the salmon fillets all over with the remaining 1 Tbs. oil. Sprinkle all over with 1/2 tsp. salt and 1/4 tsp. pepper. Put the fillets on the grill pan, skinned side up, and cook until well marked, about 5 minutes. Flip and continue to cook until opaque in the center, about 5 minutes more. Serve with the pesto.
Serve with lemony broccoli and buttered orzo.
nutrition information (per serving):
Photo: Scott Phillips