1. Cover whole potatoes with salted water.
2. Bring to a boil until almost tender (about 15 minutes).
3. Drain. Cool slightly.
4. Cut each potato lengthwise into 4 or 5 slices.
5. Melt butter and add remaining ingredients.
6. Brush grill with oil.
7. Brush potatoes genreously with butter mixture.
8. Cook potatoes, turning 2 or 3 times and brushing with butter mixture until tender and browned.