Sprinkle the fish fillets with salt and pepper, then sprinkle 1 teaspoon of thyme on top of each fillet. Place 2 slices prosciutto on work surface, overlapping slightly. Place 1 fish fillet crosswise in the center of the prosciutto; fold the prosciutto over the fish fillet (wrapped up like a blanket). Repeat with the remaining prosciutto and fish fillets.
Heat the oil in a medium ovenproof skillet over medium-high heat. Add the prosciutto wrapped fish, seam-side down. Cook until the prosciutto is brown on all sides, about 1 minute per side. Transfer the skillet to the oven and roast the fish until cooked through, about 6 minutes. Transfer to plates for serving.
Add the shallot to the same skillet; sauté over medium-high heat until beginning to brown, about 1 minute. Add the wine and the remaining 2 teaspoons of thyme. Simmer until the sauce is slightly reduced, about 1 minute. Whisk in the butter. Drizzle the sauce over the fish and serve.
Notes
If preparing this recipe as gluten free, just be sure to use a brand of prosciutto that is known to be free of gluten.