Cut each orange half crosswise into 5 to 6 half-moon slices, depending on its size. (For a prettier presentation, cut the rounded ends off of the oranges so the slices lay flat on the plate.)
Arrange the slices in a slightly overlapping circle on four plates, leaving an empty space in the center.
In a small bowl, whisk the yogurt until smooth and creamy. Whisk in the sugar, ginger, cayenne, cumin, salt and black pepper until thoroughly combined. Taste, and season with more salt and/or pepper, as desired.
Just before serving, put a generous dollop of the sauce in the center of each plate of fruit. Serve chilled.
