Preheat oven to 425 degrees.
Slice each potato into thin slices but don't allow the knife to cut all the way through. You want the bottom 1/4 inch or so to remain unsliced so the potatoes will stay together.
Place your sliced potatoes on a baking sheet.
Drizzle with olive oil. Roll your potatoes around in the oil to evenly coat each. Feel free to use more olive oil if necessary.
Generously sprinkle with salt.
Bake for 15 minutes.
Remove from oven. Top each potato with minced garlic.
Place back in the oven and bake for an additional 15 to 20 minutes. Finished potatoes should be soft with a bit of browning on the bottom.
Remove from oven and sprinkle your chopped fresh rosemary on top. Serve warm if possible (but I have served them cold and they were definitely enjoyed that way too).