To prepare the radishes, wash them really well - soak them if they just came out of the ground and are filthy - the chop off the top and bottom. Then, thinly slice either by hand using a really sharp knife or use a mandolin.
To prepare the carrots, wash, peel, and also slice off the ends. Thinly slice carrots as well, either by hand using a really sharp knife or using a mandolin.
Now, make the brine. In a small pot or saucepan, combine vinegar, water, honey, salt, crushed red pepper flakes, and mustard seeds.
Bring this mixture to a boil, stirring until the honey dissolves.
While the brine comes to a boil, pack the sliced vegetables (and optional cilantro, jalapeño, or garlic) into a wide-mouth mason jar.
Pour the mixture over the vegetables and agitate it a little to make sure that the brine gets into all the nooks and crannies of the vegetables.
Let the mixture cool to room temperature and then cover. The pickles can be eaten immediately or refrigerated for later. The pickles will keep well in the refrigerator for 3 - 4 weeks, although they will begin to lose their crispiness after about a week.