Halibut with brown butter, lemon and sage, topped with bread crumbs, in New York. For moist, juicy results with fish, frying or searing is the best option. (Karsten Moran/The New York Times)
Broiling or grilling can cause lean, white-fleshed fish like halibut (but also thick flounder fillets, snapper, grouper and large sea scallops) to dry out. 
For moist, juicy results, frying or searing is the best option. I tend to use a simple searing method for cooking firm, white-fleshed fish on the stovetop; it’s easier and cleaner than frying.
For best results, use a cast-iron pan, or any other heavy nonstick pan (even a griddle). Coat the pan with olive oil, and let it get hot before you put in the fish fillets. Leave the fish undisturbed until it is nicely golden on the first side, then flip it and cook the second side until just done.
With perfectly pristine fresh fish, you want no sauce at all — or a sauce that enhances without distracting from the fish’s flavour. Sometimes, the best solution is a drizzle of olive oil and a lemon wedge.

Halibut With Brown Butter, Lemon and Sage (Serves 4)
Halibut with brown butter, lemon and sage, topped with bread crumbs, in New York. For moist, juicy results with fish, frying or searing is the best option. (Karsten Moran/The New York Times)
About 680g halibut fillets (or other firm white-fleshed fish), cut into 4 pieces
Salt and black pepper
2 tablespoons olive oil
4 tablespoons unsalted butter
12 to 15 fresh sage leaves
2 tablespoons freshly squeezed lemon juice
1/4 cup coarse homemade bread crumbs, toasted
2 tablespoons finely chopped parsley
Lemon wedges, for serving

Season fish on both sides with plenty of salt and pepper.
Pour oil into a large, heavy skillet (preferably cast iron or nonstick) and set over medium-high heat. When oil is hot (but not smoking), swirl to evenly coat the pan, then add fish in a single layer. Let cook undisturbed for 3 to 4 minutes, until first side is nicely browned. Adjust the heat as needed to produce a steady sizzle and prevent scorching.
Flip and cook fish for about another 3 minutes, until just done. (To test for doneness, use a fork to gently probe the flesh: it should flake easily.) Transfer cooked fish to a warm platter or serving plates.
Make the sauce: Place skillet back on the stove over medium-high heat. Add butter and sage leaves. Cook butter, swirling the pan, until foamy and just beginning to brown, about 1 minute. Turn off heat and stir in lemon juice.
Spoon butter sauce and sage leaves over fish. 
Sprinkle with bread crumbs and parsley. 
Serve immediately, with lemon wedges.

The New York Times