The increased surface area exposed to the oven's heat means you get lots of crispy edges, while the base of each slice still holds soft, tender flesh>
Heat the oven to 425°F with a rack in the lower-middle position. Wash and dry the potatoes: Scrub the potatoes clean and pat them dry.
Cut slits in the potatoes, leaving the bottom intact: Cut slits into the potato, stopping just before you cut through so that the slices stay connected at the bottom of the potato. Space the slices 1/8-inch to 1/4-inch apart. (Hint: Place the potato in between two chopsticks. By cutting perpendicular to the chopsticks, your knife will stop at the perfect height with every slice.)
Arrange the potatoes in a baking dish. Brush the potatoes all over with half of the butter or other fat, including the bottoms. Sprinkle the potatoes generously with salt and pepper.
Bake the potatoes for 30 minutes. At this point, the layers will start separating. Remove the pan from the oven and brush the potatoes again with fat - you can nudge the layers apart if they're still sticking together. Make sure some of the fat drips down into the space between the slices.
Bake for another 30 to 40 minutes, until the potatoes are crispy on the edges and easily pierced in the middles with a paring knife. If you're adding any extras, stuff those into the slits and sprinkle over the top 5 to 10 minutes before the end of cooking.
Serve immediately: These potatoes are best straight from the oven while the edges are at their crispiest.