Toss the oranges with the pecan oil. Set aside for up to 1 hour before serving. Just before serving, toss in the lettuce, arugula, basil, mint, and pecans.
Do not cut the sections away from the orange membrane as our mothers did. The orange bioflavins, a newly established important nutrient, are locked in the membrane. Instead, peel the orange, then stand it on end on the cutting board and make 5 cuts from top to bottom, discard the center and cut across the membrane to cube the orange.