Preheat the oven to 350 F and grease an 8-inch square baking pan.
Whisk together the flour, sugar, and baking powder in a large bowl.
In another bowl, mix the milk, melted butter, egg, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients and stir just until combined.
Spread the batter into the prepared pan.
Mix the brown sugar and cinnamon, then sprinkle over the batter.
Dot the top with cold butter pieces.
Bake for 30 to 35 minutes until golden and set in the center.
Cool slightly before slicing and serving warm.