Place potatoes in a medium pot and cover with cold water. Add kosher salt and bring to a simmer. Cook until potatoes are just tender, about 10 – 12 minutes.
Preheat oven to 425° F. Drain potatoes and allow to cool slightly.
Once potatoes can be handled, use the bottom of a glass or the palm of your hand to gently smash the potatoes. Toss them with the oil, garlic and ginger and spread out in a single layer on a foil-lined baking sheet. Roast about 20 minutes, flipping half way through, or until potatoes are golden and crispy. Remove from oven and allow to cool slightly.
Toss roasted potatoes in a bowl with Scallion Aioli and additional salt and pepper, if desired.
Place in serving vessel and garnish generously with goat cheese crumbles, fresh scallions, and a variety of sweet and hot peppers. Serve warm or at room temperature.