Preheat oven to 425 degrees.
Slice your apples in half and remove the core and seeds.
Slice your potatoes in half. Slice again so each potato is in four pieces. If your potato was fairly large you may need to cut some of them one more time. You want your potato pieces to be about half the size of your apple slices.
Spread your apples and potatoes on a baking sheet. Drizzle with cooking fat of choice. Move your potatoes and apples around to get them all coated. Then spread them out again and make sure your apples are flesh side down.
Sprinkle with salt.
Bake for 20 - 25 minutes. (At the 20 minute mark check to see if your potatoes are done. They should give a little when you press them.)
Remove from the oven. Very gently flip your apples so the flesh side is up. They will be extremely soft. Sprinkle chopped rosemary over potatoes and apples. Serve!