Preheat grill to medium-high heat, about 400°F. Clean and oil the grates to prevent sticking.
Pat salmon dry with paper towels. In a bowl, whisk olive oil, lemon juice, soy sauce, honey, garlic, paprika, salt, pepper, and lemon zest.
Reserve 2 tablespoons of the mixture for basting. Place salmon in the remaining mixture and marinate for 10 minutes at room temperature.
Place salmon skin-side down on the grill. Close the lid and cook for 6 to 8 minutes, brushing once with the reserved glaze.
If desired, flip and grill flesh-side down for 1 to 2 minutes for light char marks. Cook until salmon flakes easily or reaches 125°F to 130°F for medium.
Transfer to a plate and rest for 2 minutes. Sprinkle with parsley and serve with lemon wedges.
Notes
For best results, leave the skin on to protect the fish on the grill. Use a fish spatula for easy removal. Substitute maple syrup for honey if preferred.