Zest two oranges. Peel and section both varieties of oranges over a bowl to catch all the juice, squeezing the juice from the pith. Peel and cut the shallot into fine slivers. Combine shallots, orange juice, lemon juice, cumin, turmeric, salt, pepper and olive oil and whisk to form a dressing; there will be extra dressing. Toss the arugula with enough dressing to moisten and arrange on a platter, garnished with currants, orange sections and zest. Drizzle with more dressing, if desired.
Use excess dressing for more salads; may substitute other types of citruses for blood and navel orange segments.