For the pesto:
Combine the basil, garlic, and pine nuts in a food processor and pulse until coarsely chopped. Pour the olive oil into the food processor while still running and process until fully incorporated. Add the cheese and lemon zest and pulse two or three times. I like to leave the pesto a little chunky. Season with salt and pepper. Use immediately or freeze in ziplock bags with the air squeezed out.
Boil your choice of pasta to ardent while the salmon is cooking.
For the salmon:
Season the flesh side of salmon filet with salt and pepper according to personal taste. Heat butter and oil over medium-high heat. Place the salmon filets, flesh side down, in the hot oil. Cook, checking frequently until golden and crispy. Turn the filets over, reduce heat to medium and continue cooking until done. The salmon is done when you press it with a finger and it feels firm. Do not overcook as it will dry out.
While the pasta is still hot add pesto until just coated. reserve the rest of the pesto and pour some over the salmon filets. If you have leftover pesto, place it in a zipper bag and squeeze out all the air. Freeze until needed. If you store it too long in the freezer the basil will darken, so use it within a couple of weeks. Hint: it is delicious as the sauce for homemade pizza.