Preheat the oven to 375 degrees F. Line a sheet pan with parchment paper.
Place the butter and brown sugar in the bowl of an electric mixer fitted with the paddle attachment and beat on medium speed for 2 minutes, until light and fluffy. With the mixer on low, add the egg, scrape down the bowl, then mix in the molasses.
Sift together the flour, baking soda, ground ginger, cinnamon, cloves, and salt. With the mixer on low, slowly add the dry ingredients to the butter mixture, mixing just until combined. Mix in the raisins and crystallized ginger. Cover the bowl with plastic wrap and refrigerate for 30 minutes.
Turn the dough out onto a very lightly floured board, form it into a disk with lightly floured hands, and cut it in half. Roll each half into a log 12 inches long and place them 3 inches apart on the prepared sheet pan. Bake for 20 minutes; the logs will still be soft in the center.
Meanwhile, whisk the confectioners' sugar with 5 to 6 teaspoons rum to make a pourable glaze. While the logs are still warm, drizzle the glaze back and forth across the logs with a teaspoon and sprinkle them with the lemon zest. Allow to cool. Cut each log crosswise into 1 1/2-inch-wide bars.