Remove trout fillets from refrigerator 15 minutes before cooking. Pat completely dry with paper towels and season both sides with salt, pepper, and dried oregano.

Heat olive oil in a large non-stick skillet over medium-high heat until shimmering. Place trout fillets skin-side down and press gently with a spatula to ensure even contact.

Cook trout for 4 minutes without moving until skin is golden and crispy. Flip carefully and cook for an additional 3-4 minutes until fish reaches an internal temperature of 63°C (145°F) and flesh flakes easily with a fork. Transfer to a warm plate and tent loosely with foil.

Wipe the skillet clean and reduce heat to medium. Add butter and cook, swirling occasionally, for 3-4 minutes until butter turns golden brown and smells nutty. Watch carefully to prevent burning.

Add sliced almonds to the browned butter and toast for 1-2 minutes, stirring frequently, until golden. Add garlic slices and capers, cooking for 30 seconds until fragrant and capers begin to crisp.

Remove skillet from heat immediately. Stir in lemon juice, lemon zest, and chopped parsley. The butter will foam and sizzle.

Place trout fillets on serving plates and spoon the browned butter, almonds, and capers generously over each fillet. Serve immediately with fresh lemon wedges alongside.