Thoroughly rinse the radishes with water. Peel them, cut off the green top and small root bottom, and then cut them into 1/8 inch thick slices. Place in the mason jar with the dried chili and garlic cloves. Heat the vinegar, water, salt, sugar, and peppercorns in a small pot until the mixture begins to boil and the salt and sugar dissolve into the liquid. Remove the pot from the heat and pour its contents into the mason jar, leaving 1/4 of an inch of head space. Tightly screw on the cap. Allow it to cool to room temperature, then label the jar with the date it was made and refrigerate it. I recommend letting it pickle for 5 days before using, but make sure to eat the contents within one month of the date they were pickled.