**Preheat the Oven:** Preheat your oven to 350°F (175°C). Grease and line a 9x13-inch baking pan with parchment paper for easy removal.
**Prepare the Dry Ingredients:** In a medium bowl, whisk together the flour, ground ginger, cinnamon, cloves, baking soda, and salt. Set aside.
**Make the Gingerbread Batter:** In a large bowl, beat the softened butter and brown sugar together with an electric mixer until light and fluffy. Add the eggs one at a time, beating well after each addition. Mix in the molasses and milk.
**Combine Wet and Dry Ingredients:** Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
**Bake the Bars:** Pour the batter into the prepared baking pan and spread it evenly. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Let the bars cool completely in the pan on a cooling rack.
**Prepare the Cream Cheese Frosting:** While the bars cool, beat together the softened cream cheese and butter until smooth and creamy. Gradually add the powdered sugar and vanilla extract, mixing until fully combined. If the frosting is too thick, add 1-2 tbsp milk to reach your desired consistency.
**Frost the Bars:** Once the gingerbread bars have cooled, spread a generous layer of cream cheese frosting over the top.
**Serve:** Cut the bars into squares and serve.