In a small mixing bowl combine salsa verde, cilantro, red onion, and avocados. Mix together and set aside.
Preheat a large cast-iron skillet over medium-high heat. Meanwhile, pat salmon dry and season with salt and pepper. Add oil to skillet; when oil is hot but not smoking add salmon skin-side down. Cook salmon 4 to 5 minutes per side. Repeat steps for remaining salmon.
Serve salmon with a large spoonful of avocado salsa verde and a squeeze of lime.