Heat oven to 425°F. Rinse, scrub, and halve potatoes. Scatter on a baking sheet, toss with olive oil, and season with salt and pepper to taste. Bake potatoes 20 to 25 minutes, or until golden. Remove from oven and set aside.
Position an oven rack on the highest rung, and heat broiler to high. Cluster the roasted potatoes together, and crumble goat cheese over the top of the cluster. Broil potatoes until cheese just begins to brown, 2 to 3 minutes. Serve immediately.