These are simple refrigerator pickles that gain zest, character and crunch over time. Aunt Hilda loved hers spicy with plenty of garlic. Select turnips that are heavy and hard, the smaller the better. Lift should last a month or so refrigerated. The pickles are delicious on their own or alongside a sandwich, a hummus or babaganouj plate with bread, or shawarma—or served with olives and cocktails.
In a small bowl, combine the vinegar, water, and salt to make a brine. Let the mixture sit for a few minutes, stirring occasionally until the salt is dissolved.
Cut the turnips and beet in half from top to bottom, and then into 1/2-inch thick wedges. Pierce the jalapeno with a knife for mild heat, or cut it in half lengthwise to expose the seeds and ribs for more heat.
Pack the turnips and beets into a quart jar layered with the garlic cloves, tucking in the hot pepper next to the glass as you go (it's pretty that way). Top with hot pepper flakes (if using instead of the jalapeno) and the pickling spice.
Pour the brine into the jar, leaving about 1/2-inch headspace. Top the jar with a lid and refrigerate for at least 3 days and up to a couple of months, shaking the jar occasionally at first to distribute the pink hue of the beet.