Step 1

Grate beets on large holes of a box grater or using grating attachment on a food processor. Place in a large bowl; stir in lemon juice, horseradish, mustard, Worcestershire, and olive oil. Let stand at least 2 hours or up to overnight. Stir in parsley.

Step 2

Whisk together carrot juice, lemon juice, Worcestershire, coconut nectar, salt, and, if using, xanthan gum in a bowl or measuring cup.

Step 3

Spoon about 2 tablespoons carrot sauce onto each of 4 small rimmed plates, swirling plates to form a circular pool of carrot sauce. Top each plate with about 3/4 cup beet tartare and 1 dill sprig.