Halibut is braised in white wine and flavored with bacon and carrots, a preparation known as "a la Barigoule" that was inspired by a Provencal peasant dish.
In a saute pan with a lid, cook bacon over medium heat until crisp and brown, and fat is rendered, about 10 minutes. Transfer bacon to paper towels to drain. Discard all but 2 tablespoons rendered fat. Add shallots to pan. Cook until they caramelize, scraping brown bits from bottom, about 6 minutes. Add garlic; cook until soft, about 4 minutes more.
Add carrots, thyme, salt, and pepper to pan; cook until just tender, about 9 minutes. Raise heat to high; slowly add wine and 3/4 cup water; stir to scrape up remaining brown bits, and cook until boiling. Reduce heat to medium; add halibut, and cover. Cook until fish is opaque and cooked through, about 8 minutes.
Transfer fish to serving plate; discard thyme sprigs. Increase heat to high. Stir in parsley, adjust seasoning, and cook 2 to 3 minutes more. Spoon vegetables and sauce over fish; garnish with reserved bacon. Serve.