Bring a small saucepan of water to a boil. Blanch fresh peas for 1-2 minutes or frozen peas for a few seconds or just long enough to take the chill off. Cool the peas in a bowl of ice water. Drain well, and set aside.
Season the filets with salt and pepper. Carefully dredge them in flour. Melt 2 tablespoons of the butter in a large nonstick skillet over medium-high heat until foaming. Cook the filets on the rounded side down first until pale golden brown, about 2 minutes. Using a fish spatula, carefully turn the fish over and cook the other side 1-2 minutes. Transfer each filet to a warm plate.
Meanwhile, melt the remaining 6 tablespoons of butter in a medium saucepan over medium heat. Squeeze in some juice from half of the lemon while swirling the saucepan. Add more juice, if you like. Remove the saucepan from the heat. Stir in the peas and parsley, and season with salt and pepper. Spoon some of the peas and butte rover each filet and scatter some chives on top. Garnish the plates with a wedge of lemon.