Using a mandoline or food processor, slice the beets into 1/16th inch slices. (you can also do this with a knife but make sure your knife is extremely sharp!). Set aside.
In a small bowl, whisk together the white wine vinegar and the lemon juice and season with salt and finely ground pepper. Continue to whisk while slowly drizzling in the walnut oil. Set aside.
Fold slices of beet in half and place, slightly overlapping each other on an individual plate or serving platter. Scatter the walnuts, preserved lemon, mint leaves and capers over the beets. Drizzle with the dressing. Serve!