1-First Step: Prepare Ingredients. Gather all ingredients. Pat the fish fillets dry with paper towels to ensure a good sear. Season both sides with salt and pepper.

2-Second Step: Heat the Skillet. Heat 1 tablespoon olive oil in a large non-stick skillet over medium-high heat until shimmering but not smoking.

3-Third Step: Pan-Sear the Fish. Place fish fillets in the skillet and cook without moving for 3-4 minutes until a golden crust forms. Flip carefully and cook another 3 minutes until the fish is opaque and flakes easily with a fork. Remove fish from skillet and set on a warm plate.

4-Fourth Step: Prepare the Sauce. Reduce the heat to medium and add the butter to the skillet. Once melted, add minced garlic and sauté for about 1 minute until fragrant. Stir in chopped shallots and cook for another minute.

5-Fifth Step: Add Flavor Components. Mix in Dijon mustard (if using), lemon juice, and heavy cream. Allow the sauce to simmer gently for 2 minutes, stirring occasionally. Adjust salt and pepper to taste.

6-Sixth Step: Combine and Warm Through. Return the fish to the skillet briefly to coat with sauce and warm through, about 1-2 minutes.

7-Final Step: Serve. Plate the fish fillets, spoon the creamy lemon butter sauce generously over the top, and garnish with fresh parsley and lemon slices. Serve instantly with your choice of steamed vegetables, rice, or mashed potatoes.