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One day ahead: Bring the honey and brown sugar to a boil in a medium saucepan, stirring occasionally. Remove the mixture from the heat and cool until lukewarm.
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In a large bowl, beat together the cooled honey mixture, the egg, and the lemon and orange peel or oil.
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Add the flour, baking soda, almonds, spices, and ground mini diced ginger, and stir until well combined. The dough will be on the stiff side, but also very sticky. Cover the bowl and refrigerate it overnight.
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The next day: Preheat the oven to 350°F. Lightly grease and line a 9" x 13" pan with parchment. The parchment will ease removing the bars in one complete piece.
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On a lightly floured surface, roll the dough into a 9" x 13" rectangle. Carefully transfer the dough rectangle to the prepared pan, either by wrapping it around the rolling pin and then unfolding it into the pan, or using a giant spatula. Don't press hard on the edges, or these areas will be dense and tough.
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Bake the bars for 20 to 22 minutes, or until a cake tester inserted in the center comes out clean.
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While the bars are baking, prepare the glaze. Stir the brandy or apple juice into the confectioners' sugar and mix until smooth. Transfer the baked bars to a cooling rack and immediately brush on the glaze with a pastry brush; let the glaze soak into the bars somewhat before applying another layer.
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Let cool completely before cutting into 1" x 2" bars.
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Store the bars in an airtight container with a slice of apple (for its softening powers). If you make the lebkuchen 2 to 3 days ahead of time, they'll taste even better. They'll last for several weeks.
