Preheat the oven to 425˚F.
Pat halibut dry with paper towel.
Spread each piece with pesto, and wrap in a slice of prosciutto.
Brush each wrapped fillet with oil and sprinkle with salt and pepper.
Set a large ovenproof skillet over medium-high heat, add a drizzle of oil and cook the wrapped filets seam-side down in the skillet for 2-3 minutes, until golden on the bottom.
Flip the filets and slide the skillet into the oven (alternatively, cover the pan to trap the heat) for about 10 minutes, until the fish is firm and the edge flakes with a fork, but the meat is still moist in the middle.