How to Make It
To prepare shallots, combine first 8 ingredients in a saucepan; bring to a boil. Pour the hot mixture over shallots; cool to room temperature. Cover; refrigerate 6 hours or overnight. Drain; discard spices.
To prepare salad, cut beets crosswise into 1-inch disks. Shave beet disks into thin ribbons using a vegetable peeler or mandoline.
Combine rind, juice, and oil in a large bowl, stirring with a whisk. Add 1/2 cup drained shallots (reserve remaining shallots for another use), beets, and parsley; toss gently to coat. Sprinkle with salt.