Pat the trout fillets dry with paper towels and season both sides lightly with the onion and chive salt and pepper.
Heat the olive oil in a nonstick skillet over medium-high heat until it shimmers. Place the trout fillets in the skillet, skin-side down.
Cook for 2-3 minutes without moving the fish, until the skin is crisp and the flesh begins turning opaque up the sides.
Add the minced garlic to the pan and cook for about 30 seconds, stirring gently around the fish. Carefully flip each fillet with a thin spatula and peel off the skin, if desired.
Add the white wine, butter, and lemon juice directly to the skillet. The liquid will bubble. Reduce the heat to low and let the fish cook for another 2-3 minutes, spooning the sauce over the top as it finishes.
The trout is done when it flakes easily with a fork and has turned opaque throughout. Remove from heat, sprinkle with fresh parsley, and serve immediately with the pan sauce.