Put the almonds, plums, apricots, and figs in the bowl of a food processor and pulse until the fruit and nuts are chopped into small pieces, but before the mixture becomes a ball, 20 to 25 pulses.
Combine the confectioners’ sugar, anise, caraway, cardamom, and salt in a medium mixing bowl. Add the nut and fruit mixture, along with the honey. Combine well using gloved hands.
Scoop the mixture into 7-gram (1/4-ounce) portions and roll into balls. If serving immediately, roll in coarse sugar and serve. If not serving immediately, put the balls on a cooling rack and leave uncovered until ready to serve. Roll in sugar just prior to serving.
Sugar plums may be stored on the cooling rack for up to 1 week. After 1 week, store in an airtight container for up to 1 month or freeze.