Put the basil, parmesan, pine nuts, and garlic into a food processor. Pulse a few times, then slowly add the olive oil while continuing to pulse, scraping down the sides if necessary. Make sure this remains somewhat chunky and doesn't turn into a puree. When it's done, mix two tablespoons of the pesto with the butter, mashing together until blended, and store the rest of the pesto in an airtight container in the fridge for up to seven days, or freeze in an ice cube tray.
For the Salmon
Heat the avocado oil in a cast-iron skillet over medium-high heat.
Salt and pepper the salmon, then place it skin-side up in the oil and cook for 3-4 minutes, depending on thickness. Flip and cook for 3-4 minutes more. Remove from pan and serve with 1 tablespoon of pesto butter on each filet.
Macros per serving: 373 calories, 1 gram net carbs, 37 grams protein, 24 grams fat.