Thinly slice the radishes (or halve them, if you prefer), and divide between 4 (11.5-ounce) jars or equivalent. The amount of radishes and brine used may vary based on the size and shape of your jars and how you slice your radishes.

Heat the vinegar, water, sugar, and salt in a medium saucepan over medium heat. Stir until the sugar and salt dissolve, about 1 minute. Pour the brine over the radishes, then divide the peppercorns and mustard seeds among the jars. Let cool and chill until ready to use. Pickled radish slices will be ready to eat in about 1 hour, radish halves are best when pickled overnight.