Slice off the leaves from the turnips and discard any wilted ones. Rinse and shake dry, then tie them together with string. Rinse the turnips but do not peel them. Slash each, making a deep X in the stem end and bury the turnips deep in the nuka paste. Press the bundle of leaves into the paste, leaving the string exposed for easy removal.
Wash the broccoli well and trim off any tough stems. Break into 1-inch flowerets before burying deep in the pickling paste. Make sure that all the vegetables are entirely covered with paste, put the lid on your pot and wait 1–1½ days for the leaves and 1–1½ days for the turnips and broccoli to mature. They will be limp and have a salty tang. Refrigerate any pickles that are not to be eaten immediately (they can be held for 2–3 days). Just before serving, rinse off any pickling paste that may be clinging to the vegetables and pat the pickles dry.
Cut the turnips into half moons ½ inch thick; chop the leaves and broccoli into bite-size pieces. Serve at room temperature with a drop or two of soy sauce.