Preheat oven to 400°F. Sprinkle fish fillets with pepper. Sprinkle 1 teaspoon thyme atop each fish fillet. Place 2 slices prosciutto on work surface, overlapping slightly. Place 1 fish fillet crosswise in center of prosciutto; fold prosciutto over fish fillet like a belt. Repeat with remaining prosciutto and fish fillet.
Heat oil in medium oven-proof skillet over medium-high heat. Add prosciutto-wrapped fish, seam side down. Cook until prosciutto is brown on all sides, about 1 minute per side. Transfer skillet to oven and roast fish until cooked through, about 5–6 minutes. Transfer to plates.
Add shallot to same skillet; sauté over medium-high heat until beginning to brown, about 1 minute. Add wine and remaining 1 teaspoon thyme. Simmer until sauce is slightly reduced, about 1 minute. Whisk in butter. Drizzle sauce over fish and serve with our Hyde Vineyard Chardonnay!
