Make crosswise cuts 1/8 in. apart across each potato, down to 1/4 in. from bottom. (For easy slicing, set a potato between two parallel rulers or dowels.) Preheat oven to 425°.
In a large bowl, coat potatoes with oil and sprinkle with salt and pepper. Place potatoes cut side up in a 9- by 13-in. baking pan. Bake until potatoes are tender when pierced, about 45 minutes (check the biggest one to be sure they're all tender). Let stand 5 to 10 minutes until cool enough to handle.
Sprinkle cheese over potatoes, pushing it into cuts, then bake until cheese is melted, 5 to 10 minutes. Transfer potatoes to a platter and let cool for a few minutes. If you like, return pan with cheese to oven and bake until cheese is crisp, about 10 minutes.
Top each potato with a small dollop of yogurt, then sprinkle potatoes and platter with bacon and chives.