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Set out 3 clean pint jars.
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Place turnips and beets in a large pot. Fill with cold water so vegetables are covered by 2-inches of water and bring to a boil. Boil 15 - 30 minutes or until vegetables are easily pierced with a fork. Drain and set aside to cool.
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When cool, use a peeler to easily remove skin under cold running water. Cut vegetables into 1/2-inch wedges (halves, quarters, or sixths, depending on the size). Pack turnips and 3 slices beets into a pint jar (to give the turnips color). Pack remaining beets in a pint jar.
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Meanwhile, halve radishes and pack into a pint jar.
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Combine vinegar, water, spices, and salt in a medium saucepan, set over medium-high heat, and bring to a boil. When mixture boils, pour liquid into vegetable-packed jars. Divide bay leaves and peppercorns between them. Allow pickles to cool to room temp, then seal and set in fridge for at least one day or up to 2 weeks.