Preheat the oven to 350º. In a small bowl, stir the hot water and baking soda until the baking soda is fully dissolved, then set aside for later. In a medium bowl, mix the molasses, oil, eggs and ginger until the mixture is fully combined.
In a large bowl, whisk together the flour, granulated sugar, salt and cinnamon, then add the brown sugar and whisk once more until no large clumps remain. Add the water and molasses mixtures to the flour mixture, and whisk together until a smooth batter forms. Pour the batter into a greased 8-inch square baking pan and bake until a cake tester comes out clean, 35 to 40 minutes.
While the cake is baking, make the rum glaze: In a small saucepan, add the evaporated milk, sugar, butter and vanilla over medium-high heat, and bring a boil. Reduce the heat to a simmer and cook until the mixture has thickened slightly, 20 minutes. Remove from the heat and whisk in the rum. Pour the rum glaze over the cake when it comes out of the oven, let sit until the glaze has been fully absorbed and the cake has cooled completely, then serve.