"Pouding chomeur is a classic Quebec dessert that translates as 'Poor man's pudding'. A syrup is poured on top of the cake mixture before baking and it turns into a delicious sauce that gathers at the bottom of the dish."
Preheat oven to 350 degrees F (175 degrees C). Grease a loaf pan.
Combine flour, baking powder, and salt in a bowl.
Mix brown sugar, water, and 2 teaspoons butter together in a saucepan; bring to a boil. Reduce heat and simmer until syrup has thickened, about 8 minutes. Remove from heat.
Beat 2 teaspoons butter in a bowl using an electric mixer until smooth and creamy. Gradually add white sugar until incorporated; beat in egg. Gradually beat flour mixture into butter mixture, alternating with milk, until batter is smooth; stir in vanilla extract. Transfer batter to prepared loaf pan; pour in the syrup on top of the batter.
Bake in the preheated oven until cake is set and syrup has soaked to the bottom, 30 to 40 minutes.