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Step 1
Remove salmon from the refrigerator and allow to come to room temperature.
Step 2
Pre-heat an air fryer to 400 degrees. Add pecans to the basket and cook for 3-5 minutes. After 3 minutes, check them every minute to make sure they're not burning. If you'd rather roast them in the oven, preheat it to 350 degrees and cook for 5 to 10 minutes on a baking sheet, checking them frequently to prevent burning. Once they're done, finely chop them with a knife or food processor and set aside.
Step 3
Meanwhile, combine the pesto ingredients in a food processor and process until finely chopped and combined. Set aside.
Step 4
Add avocado (or vegetable) oil to a large cast-iron or non-stick pan over medium-high heat. Pat salmon dry with a paper towel, and sprinkle salt and pepper over each fillet. Place the fillets in the hot pan skin-side down and let them cook, undisturbed, until the color of the filets has changed from dark pink to a more pale color about 3/4 of the way up the sides, about 3-5 minutes.
Step 5
Flip the salmon and cook an additional 1-2 minutes, until the salmon falls apart easily and the bottom has a nice sear. It's ok if the inside is still a little pink. Remove the salmon from the pan and set aside.
Step 6
Reduce the heat to medium-low and add the tomatoes and a dash of salt and pepper to the pan. Cook until they start to burst, about 3-5 minutes, stirring occasionally (it might take longer if you're not using a cast-iron pan, which retains heat better than a non-stick).
Step 7
Add garlic to the pan and cook for one minute, stirring constantly. Add pesto and cream, and cook for 2 minutes or until sauce has thickened a bit. Add romano or parmesan, stir to combine, and turn off heat.
Step 8
Remove skin from the salmon and discard, and and add the salmon back to the pan. Top with roasted pecans and juice from half a lemon, then serve.