Step 1: Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
Step 2: In a medium bowl, whisk together the flour, ground ginger, cinnamon, nutmeg, cloves, and baking soda. Set aside.
Step 3: In a large bowl, using an electric mixer, cream together the softened unsalted butter and brown sugar until light and fluffy, about 2-3 minutes.
Step 4: Beat in the molasses, then add the large egg and egg yolk one at a time, mixing well after each addition until fully incorporated. Stir in the vanilla extract.
Step 5: Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.
Step 6: Press the gingerbread cookie bar dough evenly into the prepared baking pan.
Step 7: Bake for 25-30 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out with moist crumbs, but not wet batter. Do not overbake to ensure soft, chewy bars.
Step 8: While the bars cool, prepare the vanilla glaze. In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Add more milk if needed, one teaspoon at a time, to reach a pourable consistency.
Step 9: Once the bars are completely cooled, pour the glaze over them and spread evenly. Let the glaze set before slicing and serving.