Place trout fillets in the fridge overnight or thaw under cold water for about 30 minutes. Pat dry with paper towels.
Heat olive oil in a large skillet over medium-high heat. Season trout with salt and pepper, then place skin-side down in the pan. Cook 3-4 minutes per side, until golden and flaky. Remove and set aside.
In the same skillet, melt the butter. Add garlic and cook until fragrant, about 30 seconds. Stir in lemon zest, juice, and parsley.
Return the trout to the skillet and spoon the lemon butter sauce over the fillets. Serve immediately.