Scrub potatoes and pat dry. Cut each lengthwise into sticks about 1/2 inch thick.
In a 10- by 15-inch nonstick pan, melt butter over low heat. Mix in paprika, 1/4 teaspoon salt, and 1/8 teaspoon pepper.
Add potato sticks to pan and turn in seasoned butter to coat, then arrange sticks slightly apart in a single layer.
Bake potatoes in a 425° oven until browned, turning once, about 25 minutes total.
Season potatoes with salt and pepper to taste. Serve hot.