Pat the salmon dry with paper towels and check for any remaining bones.
In a medium measuring jug, combine olive oil, soy sauce, lemon juice, honey, brown sugar, chopped parsley, minced garlic, and lemon zest. Whisk until well blended.
Place the salmon in a large zip-top bag and pour the marinade over it, ensuring it's well-coated. Seal the bag and refrigerate for 30-60 minutes.
Preheat your grill or oven. Remove the salmon from the marinade and discard the marinade. Cook the salmon skin-side down for about 10-12 minutes per inch of thickness.
Let the salmon rest for about 5 minutes before serving to allow juices to redistribute.