Preparation

Make the mayonnaise:

• Whisk the egg, lemon juice, salt, and a few grinds of black pepper in a bowl until well combined. Combine the oils and drizzle them into the egg mixture, whisking constantly. Once all the oil is added, the sauce should be shiny and thick. Fold in the remaining ingredients and season with salt and pepper to taste.

Grill the halibut:

• Meanwhile, generously coat both sides of the halibut with the oil and season both sides with salt. Let the halibut sit at room temperature for 15 minutes (while the grill heats). Grill the halibut steaks directly over the heat source (covered on a gas grill, uncovered on a charcoal grill), without touching, until they have good grill marks, 2 to 4 minutes. Flip the steaks and grill until the second sides have good grill marks and the fish is done to your liking, another 2 to 4 minutes. (Check for doneness by slicing into one of the thicker pieces.) Serve immediately with the tarragon-caper mayonnaise.

Make Ahead Tips

The mayonnaise can be made up to one day ahead and refrigerated, covered.