Season the trout fillets with salt and pepper on both sides.
In a bowl, mix together butter, parsley, garlic cloves, zest, lemon juice until well combined to make herb butter. Set aside 2 tablespoons for later use.
Preheat grill or grill pan over medium-high heat.
Grill the trout fillets skin side down first for about 4 minutes, then flip them and cook for another 3 to 5 minutes until they reach an internal temperature of 145°F (63°C).
While grilling, spread a thin layer of herb butter on top of each fillet halfway through the cooking time.
Once done, remove from heat and let them rest for about 2 minutes. Serve immediately with additional lemon wedges if desired.