Bring to a boil over high heat, then reduce heat slightly and simmer for 15-20 minutes or until the potatoes can be pierced with a fork but still have a little resistance.
Drain potatoes. Using a clean kitchen towel or parchment paper, cover each potato and give it a light "smash" with a heavy bottomed pot or the bottom of a drinking glass.
Prepare a baking pan by drizzling infused oil on the bottom and rubbing to coat. Place smashed potatoes onto the pan. Pour about 1 teaspoon of oil over each potato. Sprinkle smashed potatoes with sea salt.