1. Bring vinegar, sugar, salt, mustard seeds, coriander, red pepper flakes, cloves, and 3 cups water to a boil in saucepan. Add beet, reduce heat to medium-low, and simmer 5 minutes. Remove from heat, add sunchokes, and cool.
2. Divide vegetables among 6 8-oz. canning jars, with slotted spoon. Cover vegetables with pickling liquid, leaving 1/2-inch headspace. Place lids on jars, and refrigerate at least 24 hours before serving. Pickles will keep up to 1 month.