1 cup cider vinegar
1/2 cup water
1/2 cup sugar
1/8 teaspoon pickling spice
1/4 teaspoon mustard seeds
1/4 onion, halved
1 small bay leaf
3/4 teaspoon whole black peppercorns
3 beetroots, (1 pound without tops)
Bring all ingredients except beets to a boil in a 2- to 3-quart saucepan, stirring until sugar is dissolved.
Cover and simmer 30 minutes.
Cool marinade, then chill, covered, 1 day to allow flavors to develop.
Pour through a fine sieve into a bowl.
Cook beets in a saucepan of boiling salted water until tender, 1 to 1 1/4 hours.
Drain and cool.
Slip off skins and cut into 1/2-inch pieces.
Stir together beets and marinade, then marinate, covered and chilled, 1 day.