Preheat the oven to 350˚. Line a baking sheet with parchment paper.

Beat the butter, brown sugar, granulated sugar and molasses in a stand mixer fitted with the paddle attachment on medium speed until light and creamy. Scrape down the bowl with a rubber spatula.

Beat in 2 eggs, one at a time, then add the maple extract.

Whisk together the flour, baking powder, cinnamon, ginger, allspice, cloves, nutmeg and salt in a medium bowl. Gradually add the flour mixture to the butter mixture, beating after each addition just until combined, scraping down the bowl as needed.

Divide the dough in half and place both halves on the prepared baking sheet. Using oiled hands, shape each half into a 4½-by-8-inch rectangle (about ½ inch thick) on the baking sheet, leaving space between them. Lightly beat the remaining egg in a small bowl and brush it on the dough.

Bake until lightly browned, 25 to 30 minutes. Remove from the oven and set aside until cool enough to handle, about 15 minutes (keep the oven on). Transfer the dough rectangles to a cutting board and, using a large serrated knife, carefully slice crosswise into ½-inch-thick pieces. Arrange the biscotti on the baking sheet with a cut side facing up.

Bake the biscotti for 10 minutes, then flip and continue baking until lightly golden and dry, about 10 more minutes. Remove to a rack to cool completely.

Whisk together the powdered sugar and milk in a medium bowl. Whisk in more milk as necessary, 1 teaspoon at a time, until the glaze is thick but pourable. Use a spoon to drizzle the glaze over the biscotti on the rack, then decorate with holiday sprinkles. Allow the glaze to set completely, at least 15 minutes.