Combine the dried cherries, orange zest, apple juice and honey in a small nonreactive ovenproof saucepan and bring to a boil over moderate heat. Cook, stirring, for 5 minutes.
Put the pan in the oven and bake for about 30 minutes, stirring, until the liquid is absorbed.
Let cool slightly, then pulse in a food processor until finely chopped. Refrigerate until chilled, or for up to 4 days.
In a medium bowl, stir together the all-purpose and whole wheat flours, the baking powder, salt and cinnamon. Using an electric mixer, beat the brown sugar and butter until combined.
Add the egg and beat on high speed until thick and pale, about 5 minutes.
Add the apple sauce and dry ingredients and beat on low speed until combined; the dough will be sticky. Divide the dough in half and wrap each piece in plastic. Shape each half into a 12-inch log and refrigerate until firm.
Preheat the oven to 35
Unwrap one log and set it between 2 pieces of plastic wrap.
Roll out the dough to a 13-by-5-inch rectangle, about 1/4 inch thick.
Remove the top piece of plastic. Spoon half of the cherry filling in a 1-inch-thick stripe down the center of the length of the dough, leaving a 1/2 -inch border at each end. Using the plastic wrap, fold up one side of the dough to partially cover the filling and flatten slightly. Lift the other side to cover the filling, slightly overlapping the first piece of dough, and pinch the sides together to seal. Tuck in the ends. Repeat the process with the remaining dough and filling.
Roll the filled logs onto a baking sheet, seam sides down, and flatten to form 12-by-2-inch logs.
Brush each lightly with the egg white and sprinkle with coarse sugar.
Bake for about 20 minutes, or until golden and the tops begin to crack.
Let cool on the baking sheet for 5 minutes. Using a serrated knife, trim the ends and slice each log into sixteen 1-inch bars.
Notes: ONE BAR: Calories 63 kcal, Protein 1 gm, Carbohydrate 13 gm, Cholesterol 9 mg, Total Fat .9 gm, Saturated Fat .5 gm
