Hot Fudge Chocolate Pudding Cake

1 cup all-purpose flour (or plain flour)
1/2 cup white granulated sugar
1/4 cup cocoa powder
2 teaspoons baking powder
1/4 teaspoon salt
3/4 cup milk
1/4 cup unsalted butter, melted
1 teaspoon pure vanilla extract
1/2 cup white granulated sugar
1/2 cup packed light brown sugar
3 tablespoons cocoa powder (I like unsweetened cocoa powder. (*See notes)
1-1/4 cups boiling water
Preheat oven to 350°F (175°C). Lightly grease a 9-inch square baking pan*. Pre-boil water in a kettle while preparing cake.
FOR THE CAKE: Combine 1/2 cup granulated sugar with the flour, cocoa powder, baking powder, and salt. Add in the milk, butter, and vanilla; whisk until smooth and fairly lump-free.
Pour the batter into the prepared baking pan or dish and spread evenly.