Preheat oven to 400°F (200°C) or air fryer to 360°F (180°C).
Wash potatoes and boil in salted water until just fork-tender, about 10 minutes.
Drain potatoes and place in a medium bowl; toss with melted vegan butter, garlic powder, gochugaru, and a pinch of sea salt.
Spread potatoes on a baking sheet and gently crush with the bottom of a jar or glass until they burst but remain mostly intact.
Bake in oven or air fry until crispy, about 20 minutes.
While potatoes cook, combine chopped shallots and lime juice in a small bowl and let pickle for 5 minutes.
In another bowl, whisk together vegan mayonnaise, gochujang paste, vegan fish sauce, and coriander leaves.
Remove crispy potatoes and let cool for 5 minutes before transferring to a serving plate or bowl.
Dress potatoes with half of the sauce, sprinkle with chives and black sesame seeds if using, and serve the remaining sauce on the side.