Boil the beets until just tender. Drain well and cool in ice-cold water. Trim the very top and bottom off each beet. Peel off the skins with your fingers. Make a bed of leaf lettuce on each of 4 plates. Thinly slice the beets and arrange in an overlapping layer on top of the lettuce. Combine the next 7 ingredients in a small bowl.
Season the scallops with salt and pepper. Place the 2 Tbsp. of oil in a pan and set over medium-high heat. Add the scallops and sear 1 to 2 minutes on either side, or until just cooked through. Set 3 scallops on top of the beets on each plate. Drizzle each salad with the dill vinaigrette and serve.