Place salmon on a plate and pat dry with clean paper towel.
Drizzle with 1 tablespoon olive oil and rub all over.
Sprinkle with kosher salt and ground black pepper.
Bring a large cast iron skillet to medium-high heat. Add 1 tablespoon olive oil; swirl to coat.
Add salmon skin-side up and let cook 2-4 minutes.
Flip and use a spoon or brush to add pesto on top of each piece of salmon (you can really use as much or as little as you like).
Place in the oven, middle rack and uncovered, for 10-14 minutes or until the internal temperature is 145 degrees F - for thinner piece of salmon it may take a little less than 10 minutes).
Remove and let rest 5 minutes.
Serve immediately and feel free to put extra pesto on top after cooking if so desired.
Notes
Salmon: I recommend using fresh fish, purchased the day you plan on cooking it for best results. Frozen fish works too, but just make sure it is fully thawed and there isn't any excess moisture and the resulting dish will be watery.