Clean the grill grates thoroughly and lightly oil them to prevent the potatoes from sticking. You can dip a folded paper towel in cooking oil and use tongs to rub it across the grates.
Preheat your grill to medium-high heat (around 375-400°F). If you're using a charcoal grill, ensure the coals are evenly lit and glowing.
Cut the scrubbed russet potatoes into wedges. You can leave the skin on for added texture and flavor.
If using butter, melt in a small skillet and add the garlic powder, rosemary, thyme, salt, and pepper. Stir for about 30 seconds to allow the flavors to bloom. Remove from the stove and mix well to create a marinade. If using olive oil, skip this step.
Add the potato wedges to the bowl, season to taste, then add the marinade. Toss them gently until they are well coated with the mixture.
Place the coated potato wedges directly on the preheated grill. Make sure to arrange them in a single layer for even cooking.
Cook undisturbed for 2-3 minutes per side for good sear and grill marks. Reduce heat and continue grilling, turning them occasionally until golden brown, crispy on the outside, and tender on the inside. Cooking times may vary depending on the thickness of the wedges.
Once cooked, remove the potato wedges from the grill and transfer them to a serving dish.
Sprinkle minced parsley over the grilled potato wedges for added flavor.
Serve the grilled potato wedges hot as a side dish or appetizer. They pair well with dipping sauces like ketchup, aioli, or sour cream.