1. Prepare grill for indirect grilling, heating one side to medium-high and leaving one side with no heat.
2. Peel potatoes, and cut lengthwise into 1/2-inch-thick slices. Combine potatoes, 1 tablespoon oil, 1/4 teaspoon salt, and 1/4 teaspoon black pepper; toss.
3. Place potatoes on grill rack over unheated side; close lid. Cook 12 minutes on each side or until tender. Move potatoes to heated side; grill 2 minutes on each side or until charred.
4. Combine 1/4 cup oil, 1/2 teaspoon salt, 1/4 teaspoon black pepper, juice, and next 4 ingredients (through jalapeño) in a large bowl. Slice potato slices into strips. Add potatoes, cabbage, and remaining ingredients to bowl; toss.