STACKS: Peel and cut off stem end of each beet. Slice into ¼-inch circles. Roll out a 12-by- 14-inch sheet of foil, and top with a 10-by-12-inch sheet of parchment. Pile sliced beets onto parchment, drizzle with olive oil, and season with salt and pepper. Fold up to seal within parchment. Place in a toaster oven, and set to 325°F (or use a preheated conventional oven). Bake 30 to 40 minutes, or until beet slices are fork tender. Remove from toaster and let cool, uncovered.
Meanwhile, slice each plum in half, from stem end to bottom, and remove pit. Slice halves into discs ¼-inch thick. Cut tomatoes into ¼-inch slices. Slice mozzarella into circles ¼-inch thick.
Stack cooked beets, plums, and tomatoes, along with mozzarella, in any order (we like to start with beets at the base, followed by plum, mozzarella, tomato, mozzarella, and beet). Repeat with remaining ingredients for desired servings. Place stacks on a sheet tray.
LEMON-HERB DRIZZLE: In a small bowl, whisk together oil, lemon juice, mint, oregano, and shallot. Season with salt and pepper.
TO SERVE: Spoon 1 tablespoon of lemon-herb drizzle over each stack. With a spatula, carefully transfer each stack to a plate.
In a medium bowl, combine frisée and sprouts. Spoon 2 tablespoons of lemon-herb drizzle over salad greens, season with salt and pepper, and toss lightly. To plate, place a small pile of the dressed salad next to each stack. Spoon additional vinaigrette over stack and salad, as desired.