Place whole unpeeled potatoes in a pot.

Cover potatoes with cold water by at least 2 inches.

Bring to a boil over high heat.

As soon as water boils, set a timer and cook potatoes for 10 minutes.

Drain the potatoes.

Cover the potatoes with cold water and let cool to room temperature.

Preheat oven to 425 degrees Fahrenheit.

Combine olive oil, garlic, sweet paprika, and smoked paprika (if using) in a bowl.

Place a potato on a large spoon.

Use a sharp knife to make 1/8-inch-thick slices in the potato, crosswise, without cutting through the bottom.

Repeat with remaining potatoes.

Place potatoes on a piece of foil.

Brush generously with the paprika oil, using fingers to separate slices and let oil drip down.

Sprinkle with salt, making sure that it gets between the slices.

Place on a baking sheet and bake for 20 minutes.

Remove from oven and brush again with oil.

Use oven mitts to gently squeeze potato and open up the slices.

Sprinkle again with salt.

Bake 10 to 20 minutes more, until potatoes are cooked through.

Serve whole or halved.