Pat the cod dry with a paper towel. Sprinkle it with salt, pepper, paprika and garlic powder, then rub it with the olive oil. Leave at room temperature while preheating the grill.
Preheat grill or grill pan to medium-high heat. Coat grill grates with olive oil.
Place cod onto the preheated grill. Grill for 4 minutes, then use a spatula to carefully lift the cod off the grill. If it feels sticky, allow it 1-2 more minutes until it releases easily. Flip the cod and cook until the cod starts to flake and reaches internal temperature of 130°F, about 2-4 more minutes. Use a spatula to carefully remove the cod off the grill.
Allow to rest for 5 minutes, then serve with fresh parsley and lemon wedges, if desired.
Tip: Take extra care to grease the grill grates this makes all the difference in your cod sticking to the grill!