Preheat your oven to 350°F (180°C). Grease a 9x9-inch (23x23-cm) square cake pan and line with parchment paper.
In a medium bowl, whisk together the flour, baking powder, ginger, cinnamon, nutmeg, cloves, and salt. Set aside.
In a large bowl, beat the softened butter with an electric mixer until creamy. Add the brown sugar and granulated sugar and beat until light and fluffy, about 2-3 minutes.
Beat in the eggs one at a time, scraping down the sides of the bowl as needed.
Beat in the molasses until well combined.
Gradually add the dry ingredients to the wet ingredients, alternating with the hot water, starting and ending with the dry ingredients. Mix until just combined.
Pour the batter into the prepared cake pan and bake for 30-35 minutes or until a toothpick inserted into the center of the cake comes out clean.
Allow the cake to cool in the pan for 10 minutes, then remove the cake from the pan and transfer it to a wire rack to cool completely.
To make the glaze, whisk together the powdered sugar, milk, and vanilla extract in a medium bowl until smooth. Drizzle the glaze over the cooled cake and allow it to set before slicing and serving.
Serve the Ginger Cake with a dollop of whipped cream and some fresh fruit if desired. Enjoy!