Adjust oven rack to middle position and heat oven to 200 degrees. Microwave Brussels sprouts, 1 tablespoon water, 1 ½ teaspoons salt, and ¼ teaspoon pepper in covered bowl, stirring occasionally until Brussels sprouts are just tender, about 6 minutes. Drain well.
Cook bacon in 12-inch nonstick skillet over medium-high heat until crisp, about 5 minutes. Using slotted spoon, transfer bacon to paper towel-lined plate, and set aside.
Add shallot to bacon fat left in skillet and cook over medium-high heat until softened, about 1 minute. Stir in garlic and thyme, and cook until fragrant, about 30 seconds. Add drained Brussels sprouts and cook until spotty brown, about 3 minutes. Stir in crisp bacon, and then transfer to oven safe serving platter and keep warm in oven.
Wipe skillet clean with paper towels. Combine coriander, mustard, 2 teaspoons salt, and ½ teaspoon pepper in bowl. Pat trout dry with paper towels and season with spice mixture. Heat 2 tablespoons ghee in now-empty skillet over medium-high heat until shimmering.
Place 2 fillets flesh side down in skillet and cook until browned on first side, about 3 minutes. Carefully flip fillets and cook until browned on second side and until trout flakes apart when gently prodded with paring knife, about 3 minutes; transfer to platter in oven. Repeat with remaining 2 tablespoons ghee and remaining 2 fillets. Serve with lemon wedges.
*We recommend using a fish spatula to remove the fish from the cast iron pan.