Heat oil in a Dutch oven over medium-high. Add onion, ginger, and garlic; cook, stirring often, until softened, 5 to 6 minutes. Add curry powder; cook, stirring constantly, 1 minute. Stir in collard greens, coconut milk, vinegar, salt, and sugar. Increase heat to high; bring to a boil. Reduce heat to medium-low; cover and simmer until tender but not mushy, 40 to 45 minutes.

Transfer collard greens to a serving bowl using a slotted spoon or tongs. Top with flaked coconut, and sprinkle with Espelette.