Put a large pot of whole, unpeeled (but cleaned) potatoes in cold water over high heat, and allow to boil until almost tender when pierced with a fork. Drain the potatoes, pat dry with a kitchen towel, and cut into quarters, so that you have large wedge-style fries.
Grill Method: In a small bowl, mix the finely chopped rosemary and salt into the oil. Using the grill brush, coat both sides of the wedge with oil (not the peel side). Grill over medium heat for 4 minutes on each side, or until golden brown and tender when pierced with a fork.
Oven Method: Preheat oven to 425 degrees. In a small bowl, mix the finely chopped rosemary and salt into the oil. Using a basting brush, coat both sides of the wedge with oil (not the peel side). Place potato wedges on a nonstick (ungreased) baking sheet. Bake until the wedges are golden and crisp on the outside, approximately 35 minutes.
Meanwhile, for the Aioli:
Whisk all of the remaining ingredients together to incorporate, slowly drizzling in the olive oil last, while stirring.