Prepare radishes, jalapeños, garlic, and ginger root; layer in a pint-sized jar.
Put the rest of the ingredients into a small saucepan over low heat. Stir the brine and heat until the salt and honey dissolves. The idea is to keep the temperature of the brine below 100 degrees so that the raw honey's nutrients remain intact. Use a candy thermometer if you have one to check the brine's temperature.
Pour the brine into the jar. Cover and let it cool down, then refrigerate. These pickles will be tasty enough to enjoy within a couple of hours, but will absorb more flavor the longer they sit.
Eat within a week or so for best results. If you keep longer, the radishes may get too limp.