The cute little island is called Lítla Dímun. It’s part of the Faroe Islands, which is a self-governing archipelago about 450km southeast of Iceland. Despite the proximity, the islands are actually owned by Denmark.
Supposedly, visitors can visit most of the islands, but Lítla Dímun is off limits due to wildlife preservation and pretty frequent has inclement weather which obstructs the view of the island. Atlas Obscura recommends getting a glimpse of the island from the villages of Hvalba or Sandvík, on the island of Suðuroy. But, looking at maps, it appears you can likely trek from Trongisvágur to Hvannhagi, a spot the overlooks the bay, from what looks like the remnants of ancient caldera:
