In a large, nonreactive saucepan, combine the honey, brown sugar, granulated sugar, and butter and place over medium-high heat, stirring occasionally, until the sugar is dissolved, the butter is melted, and the mixture just begins to boil. Remove the pan from the heat and let the mixture cool for 15 minutes.

In a medium bowl, sift together the flour, baking soda, cinnamon, cardamom, cloves, nutmeg, and ginger. Set aside.

Stir the sliced almonds, candied orange peel, egg, orange juice, orange zest, and vanilla and almond extracts into the cooled honey mixture. Add the dry ingredients and stir until blended. Place a piece of plastic wrap directly on the surface of the dough. Seal the top of the pot with another piece of plastic wrap and let the dough stand at room temperature (do not refrigerate) for 8 hours, or overnight.

Position a rack in the center of the oven and preheat to 350 degrees F. Butter and flour a 9-inch square baking pan. Transfer the dough to the pan and, with a spatula, spread it into an even layer. Bake the lebkuchen for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean. While the bars are baking, make the glaze.

In a medium bowl, whisk together the confectioners' sugar, orange juice, ginger, and vanilla extract until smooth.

When the bars have baked, place the pan on a wire rack. Using a small, offset metal spatula, spread the glaze onto the warm bars in an even layer. Let the bars cool completely.

Using a sharp knife, cut the glazed square into twenty-four 1-1/4 by 1-3/4 inch rectangles.