Wash and thinly slice the radishes into 1/8-inch rounds using a sharp knife or mandoline. Pack the sliced radishes into clean jars, dividing them evenly. I like to pack them fairly snugly but not so tight that the brine can't flow through—this helps them pickle evenly.

Combine the white vinegar, water, sugar, and salt in a pot and bring to a boil over medium-high heat. Once boiling, stir for about 1 minute until the sugar and salt are completely dissolved. You'll notice the liquid becomes clear and slightly syrupy—this is when you know everything has dissolved properly.

While the brine heats, distribute the peppercorns, mustard seeds, smashed garlic cloves, and red pepper flakes evenly among the jars with the radishes. Once the brine is ready and still hot, carefully pour it over the radishes and spices until they're completely submerged. I find that pouring slowly and using a wooden spoon to guide the liquid helps the aromatics distribute evenly throughout the jars.

Let the jars sit at room temperature until the brine has cooled completely, then transfer them to the refrigerator. The radishes will develop mild pickled flavor after about 1 hour of chilling, but they taste even better after sitting overnight as the flavors deepen and mellow.