Season both sides of the salmon fillets with salt and black pepper.
Grate lemon peel to get 1 tsp of fresh lemon zest and squeeze two lemons to get 4 tbsp of lemon juice.
In a large, light-colored pan, melt unsalted butter over medium heat until it browns (about 5 minutes).
Add the salmon fillets and cook for 3-4 minutes on the first side, then flip and cook for another 2-3 minutes on the second side.
In the last 2 minutes of cooking, add lemon zest and lemon juice. Spoon the sauce over the salmon as it cooks.
Transfer the cooked salmon to a serving plate and drizzle with the pan sauce.
Garnish with freshly chopped parsley before serving. Enjoy the tender, flaky salmon with the lemon brown butter sauce.
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