Wash potatoes and cut into thick long wedges. Place in a large pot of cold water and let soak for 3 minutes. Drain, rinse well, and fill the pot back up with cold water making sure to cover potatoes by at least 2 inches. Add 1 tsp salt to water, stir well.
Place the pot with potatoes over a high heat burner. Bring water to a boil. Let boil for 8 minutes. NOTE: You don’t want them to fall apart when pierced with a fork. You can cook them for up to 10 minutes depending on how thick your wedges are cut. Drain water from potatoes and place on a cutting board to let potatoes dry completely.
In a large mixing bowl combine ground black pepper, garlic powder, onion powder, Italian seasoning, smoked paprika, salt, lemon juice, ground mustard, dried parsley and olive oil. Use a whisk to mix.
Add potatoes to the bowl and gently toss in olive oil marinade.
Heat your grill to medium heat, about 375 degrees and brush the grill grate with olive oil.
Carefully place potatoes on the grill. Close the grill cover and let cook for 5 minutes. NOTE: Save the leftover olive oil marinade and set the bowl aside. Lift the grill cover and use a spatula to flip each potato over to the other side. Close the grill cover and let cook for 5 additional minutes.
Remove the potatoes from the grill and place back into the leftover olive oil marinade bowl. Pour melted butter over the potatoes. Sprinkle 2-3 tbsp finely chopped parsley over the top of the butter and toss the potatoes gently to combine.
Serve immediately.