1. Heat skillet over medium heat; add garlic and toast 15 to 18 minutes, turning, until skin is charred in spots and garlic feels soft when pressed with a finger. Cool.
2. Gently squeeze garlic cloves from skins; transfer to food processor. Add bread, mayonnaise, lemon juice, shallot, 1/4 teaspoon salt, red pepper and saffron, and puree, gradually adding water through feed tube until smooth. Transfer to small serving bowl.
3. Meanwhile, prepare grill according to manufacturer's directions for direct grilling.
4. Bring potatoes and enough cold salted water to cover to a boil in large saucepan. Cook 5 to 6 minutes, until potatoes are just tender; drain in colander and cool.
5. Gently toss potatoes with oil, 1/2 teaspoon salt and 1/2 teaspoon pepper in a large bowl. Skewer 4 to 6 potatoes on 6 skewers.
6. Oil grill. Grill potatoes, turning occasionally, until browned on all sides, 16 to 18 minutes. Slide potatoes off skewers onto serving platter. Sprinkle with parsley, if desired. Serve with aioli. Makes 12 appetizer servings or 6 side servings.