Preheat the oven to 450° Fahrenheit
In a food processor, blitz together basil, garlic, almonds, parmesan, pecorino, 1 ½ tablespoon lemon juice, 1 ½ tablespoon lemon zest, salt.
Add the extra-virgin olive oil into the food processor (start with 1 cup) and blend until combine. To get a thinner consistence continue adding more olive oil. Set aside.
Season Salmon with salt and pepper.
Add 1 ½ tablespoon extra-virgin olive oil in a large skillet. Heat until hot, turn the dial to medium heat. Place salmon into the skillet with the skin-side down. Cook for 3-4 minutes. Remove skillet from stove top and place in oven. Cook for 8-10 minutes or until thoroughly cooked.
Slice the remaining lemon. Decorate the top of the salmon with lemon pesto and lemon slices.