To make the trout and crust: Preheat the oven to 350 degrees F.

Put the flour and egg in separate shallow dishes. Mix the oats and horseradish together in a third shallow dish.

Pat the trout fillets dry with a paper towel and season with salt and pepper. (If the fillets taper down to a very thin tail, fold the tails back to make a more uniformly thick fillet.)

Dredge the flesh sides of the trout fillets (leave the skin sides dry) in the flour then egg, and finally in the oat mixture. Shake of any excess. Put on a piece of waxed paper or baking sheet.

Heat 1 large skillet over medium heat. Add the oil and heat until hot. Lay the fish in the skillet oat-side down and cook until golden brown, about 3 minutes. Add the butter during the last minute of cooking. Turn, cook on the other side, until golden, about 1 minute more. Transfer to a baking sheet, place in the oven, and bake until cooked through, about 3 minutes.

To make the sauce: Drain off any oil left in the skillet; add garlic and chives and saute for 1 minute. Add the Cognac away from the heat. Return the skillet to high heat, step back and flambe. Scrape up any browned bits that cling to the pan with a wooden spoon, and simmer until syrupy. Add the heavy cream, bring to a boil, lower the heat, and simmer until thickened, about 3 minutes. Whisk in the mustard, parsley, salt, and thyme. Season with the pepper, to taste.

Divide the sauce among 4 plates, place the fish on top, drizzle on the Worcestershire sauce, and serve.