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Leaving the skin intact, cut the salmon into four 5-6 ounce filets.
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Add the flour, ¼ teaspoon of salt, and ¼ teaspoon of black pepper to a large, shallow bowl. Whisk together until combined. Dip each salmon filet into the flour and coat all sides. Shake off any excess. Reserve the remaining flour.
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Add 2 tablespoons of butter to a large skillet over medium heat. Once melted, add the salmon filets, flesh-side down, and cook for 4-5 minutes. Flip them over and continue cooking for another 3-4 minutes, or until cooked through.
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Remove the salmon from the skillet and place on a separate plate.
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Add 2 additional tablespoons of butter to the skillet along with the garlic. Saute for 30 seconds, or until the garlic becomes fragrant. Whisk in 2 tablespoons of the reserved flour and then quickly pour in the lemon juice. Pour in the broth, ¼ cup at a time, whisking well after each addition.
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Add the salmon back into the skillet along with the capers and heat it back up for 2-3 minutes. Just before serving, top with lemon zest, if desired. Enjoy!