Thresher shark steaks make for a hearty, mildly flavored, simple meal similar to mako shark or swordfish steaks. These sturdy cuts hold up better on the grill or in the pan than flakier fish, and they do well under the broiler, too. Their high fat and moisture content help prevent them from drying out with dry-heat cooking methods, but keep a close eye on them because they do dry out with overcooking. If you like, thresher shark steaks do well with a 20- to 30-minute soak in citrus juice, soy or teriyaki sauce, wine or other seafood marinade.
On the Grill
Scrape your grill clean and grease it well with nonstick spray to prevent imparting off flavors and to keep the steak from sticking. Preheat to medium-high.
Pat both sides of the thresher shark steak dry with paper towels. Brush it with cooking oil or melted unsalted butter. Season both sides with salt, freshly cracked black pepper and any herbs, spices or aromatics you'd like to use; thyme, oregano, basil, tarragon, sage, blackening, minced garlic and citrus zest all work well on shark steaks.
Lay the steak on the grill and let the grill marks sear into the flesh for about 2 1/2 minutes. Rotate the steak 90 degrees and sear in a crosshatch pattern for about another 2 1/2 minutes.
Turn the shark over with a spatula and continue cooking it until the flesh is opaque and flaky throughout. This should take about another 5 to 6 minutes.
Beneath the Broiler
Preheat your oven's broiler for about 10 minutes. Coat the rack of your broiler tray with nonstick spray.
Blot the thresher shark steak dry with paper towels, then drizzle both sides with cooking oil or melted unsalted butter. Pat both sides with salt, pepper and any other flavoring agents you'd like to use. Center the steak on the broiler pan.
Place the shark into the oven with its surface is 4 inches directly below the broiler. Cook it for 5 minutes.
Turn the steak over with a spatula. Broil for another 5 minutes or so, just until the flesh becomes flaky and opaque all the way through.
In the Pan
Place a cast-iron or stainless steel skillet on a burner over medium high heat. Let it heat up for a few minutes.
Dry the thresher shark steak using paper towels. Coat it with cooking oil or unsalted butter, then apply salt, pepper and other desired seasonings.
Put the shark in the pan and leave it in place.. Sear it for about 4 minutes, until the bottom develops a well-browned crust.
Turn the steak with a spatula and sear the other side for another 4 minutes or so, just until the second side develops a matching crust and the meat is opaque and flaky.