Preheat oven to 400°F.
Heat 2 teaspoons oil in a medium ovenproof skillet over medium-high heat. Add onion and cook, stirring often, until just starting to soften, 4 to 6 minutes. Add wine, increase heat to high and cook, stirring often, until the wine is slightly reduced, 2 to 4 minutes.
Place fish on top of the onion and sprinkle with thyme, salt and pepper. Cover the pan tightly with foil; transfer to the oven and bake for 12 minutes.
Toss the bread with the remaining 2 teaspoons oil, paprika and garlic powder in a small bowl. Uncover the fish; top with the bread mixture and cheese. Bake, uncovered, until the fish is just cooked through, 8 to 10 minutes.
Ingredient Note:Overfishing and trawling have drastically reduced the number of cod in the Atlantic Ocean and destroyed its sea floor. A better choice is Pacific cod (aka Alaska cod); it is more sustainably fished and has a larger, more stable populace (mbayaq.org/cr/seafoodwatch.asp).