Cut the greens off about 1/4 inch above where they join the radishes, leaving a tiny decorative piece of green attached to each radish. Trim off the root tips. Put the radishes in a saute pan just large enough to hold them in a single layer and pour over enough broth or water, about 1 cup, to come halfway up the sides of the radishes. Add the butter to the pan and sprinkle over sugar and salt. Bring to a simmer over high heat, turn down the heat to medium, and place a sheet of aluminum foil or wax paper loosely over the radishes. Simmer for about 15 minutes, or until the radishes can be poked through with a skewer or paring knife but still offer some resistance. If they are done but there is still liquid in the pan, remove foil or paper and turn the heat up high to quickly evaporate the liquid. When all the liquid has evaporated and the radishes start to brown on 1 side, toss them, or very gently stir until they are lightly browned on all sides and a thin layer of caramelized sugar has attached to the bottom of the pan. Pour about 2 tablespoons water into the pan and quickly toss or stir the radishes over high heat to dissolve the sugar caramelized on the bottom of the pan and get it to coat the radishes in an even layer. When the water has evaporated, grind over some pepper and serve immediately.
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