In a medium bowl, whisk together the flour, baking powder, salt, and granulated sugar.
In another bowl, mix the milk, melted butter, and vanilla extract until well combined.
Gradually add the wet ingredients to the dry ingredients, stirring until just combined.
Preheat your oven to 350°F (175°C). Grease a 9x9-inch baking dish.
Pour the batter into the prepared dish, spreading it evenly.
In a separate bowl, combine the brown sugar and hot water, stirring until the sugar is dissolved.
Carefully pour this mixture over the batter in the baking dish; do not stir.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown and a toothpick inserted into the cake portion comes out clean.
Allow to cool for about 10 minutes before serving.