In a dry non-stick skillet heat walnuts over medium heat. Stir often and watch carefully. When they start to brown and you can smell them they are done. This may take 8-10 minutes. Set walnuts aside to cool.
Heat the 1 Tbsp olive oil and 1 Tbsp sherry vinegar in the skillet over medium heat. Saute shallot and red onion until golden and caramelized. Stir occasionally. This may take up to 20 minutes. Remove from heat and allow to cool.
Mix all the vinaigrette ingredients together and shake well.
Slice the duck breast thinly. Microwave 2 minutes on high and allow them to cool. Aim for about 18 slices.
Mix the greens, pomegranate kernels and walnuts together. Divide greens mixture among 6 plates. Arrange 1/6 of duck slices in the center of the greens on each plate.