Preserved lemon – less tart than fresh ones but with a more concentrated lemon flavor – infuses the simple butter sauce served with these delicate halibut fillets.
Put the flour on a large shallow plate. Season both sides of the fish fillets with salt and pepper. Dredge the fish in the flour and shake off the excess
Heat the clarified butter in a 12-inch nonstick skillet over medium-high heat until bubbling. Put the fish fillets in the pan and cook until just done, 2 to 3 minutes per side.
Add the unsalted butter to the skillet over medium heat and let melt, about 1 minute. Stir in the preserved lemon and remove from the heat.
Arrange the fish on a warm serving platter. Top with the parsley. Pour the preserved lemon butter evenly over the fillets. Serve immediately.