Preheat your oven to 350°F. Line a 9x9-inch baking pan with parchment paper, allowing some overhang for easy removal later.
Whisk together the flour, ground ginger, cinnamon, nutmeg, baking soda, and salt in a bowl.
In a separate bowl, cream the softened butter and light brown sugar until light and fluffy, about 3-4 minutes. Mix in the molasses, egg, and vanilla extract until well combined.
Gradually fold in the dry ingredients until just incorporated, being careful not to overmix.
Transfer the dough to the prepared pan, spreading it out evenly. Bake for 18-22 minutes, or until a toothpick comes out with a few moist crumbs. Avoid overbaking to keep the bars moist.
Cool the bars completely in the pan. For the glaze, whisk together the powdered sugar, milk, and vanilla extract until smooth, adjusting the milk or sugar for desired consistency. Drizzle over the cooled bars.
Let the glaze set for 15-30 minutes. Lift the bars out using the parchment paper and cut into squares.