Put an oven rack in the center of the oven and preheat the oven to 450 degrees F.
Pat the halibut dry with a paper towel. Spread the flour in 1 shallow dish, beat the egg with 2 tablespoons water in another, and put the Parmesan cheese in a third.
Heat a medium oven-proof skillet over medium-high heat. Add the butter or oil and heat until hot but not smoking. Meanwhile, coat the halibut with flour, shaking off the excess; repeat with the egg mixture and Parmesan. Add the fish to the pan and cook until golden on both sides, 1 to 2 minutes per side. Transfer the skillet to the oven and cook until slightly crispy, 4 to 5 minutes. Serve hot.