Heat the oven to 350°.
Line a 13- by 9-inch pan with a foil (or parchment paper) sling: In the pan, crisscross two foil pieces so that each edge extends 1 or 2 inches beyond the lip of the pan. Smooth the foil onto the pan edges and into the corners. Grease with butter.
In a medium bowl, whisk together the flour, ginger, cinnamon, cloves, baking soda, and salt.
In a separate bowl, using a mixer on high, beat the butter and sugars until light and fluffy, about 3 minutes. Beat in the eggs, one at a time, then add the vanilla extract and molasses. Turn off the mixer, scrape down the bowl with a rubber spatula, as needed, then continue mixing until all is combined. With the mixer on low, slowly add the dry ingredients, mixing until everything is just combined.
Spread the batter evenly in the prepared baking pan. Bake until a toothpick inserted in the center comes out clean, 35 to 45 minutes.
Leave the gingerbread in the pan until it cools completely, about 45 minutes to an hour. Use the foil sling to lift the gingerbread from the pan. Cut it into rectangular bars.
In a medium bowl, whisk together the glaze ingredients. Pour the glaze into a ziplock bag with a corner snipped off and drizzle it onto each bar.