DRAIN beets, reserving juice. Set beets aside for another use. COMBINE beet juice, vinegar, sugar and spices in medium saucepan. Bring to a boil; STIR until sugar is dissolved. REDUCE heat and simmer 5 minutes.
ARRANGE eggs in 1-quart heat-proof glass jar with tight fitting lid. POUR hot marinade over eggs. Cover tightly. Allow to cool to room temperature 1 hour. Refrigerate to blend flavors, at least several hours or up to one week.
Easy 12-Minute Method for Hard-Boiled Eggs: Place eggs in a saucepan large enough to hold them in a single layer. Add cold water to cover the eggs by 1 inch. Heat over high heat just to boiling. Remove from the burner. Cover pan. Let eggs stand in hot water for about 12 minutes for large eggs (9 minutes for medium eggs; 15 minutes for extra large eggs). Drain. Shock the eggs in a bowl of ice water to cool them immediately. Hard-boiled eggs are easiest to peel right after cooling.
Pickle hard-boiled eggs in a brilliant beet juice for a colorful appetizer or snack for holidays and entertaining.
Very fresh eggs can be difficult to peel. To ensure easily peeled eggs, buy and refrigerate them a week to 10 days in advance of cooking. This brief “breather” allows the eggs time to take in air, which helps separate the membranes from the shell.
Hard-boiled eggs are easiest to peel right after cooling. Cooling causes the egg to contract slightly in the shell.
Use a clean tool to remove eggs from the brine. Do not pour off brine to retrieve eggs or re-use the brine. Pack eggs into sterilized glass jar that are labeled with the date packed. Keep continuously refrigerated, and use within 3-4 months.