Preheat the oven to 350°F (175°C). Grease a 9x13 inch baking pan.

In a mixing bowl, whisk together flour, sugar, baking powder, and salt.

Add melted butter, milk, and eggs to the dry ingredients and mix until just combined.

In a small bowl, mix together brown sugar and cinnamon.

Pour half of the cake batter into the prepared pan. Sprinkle half of the cinnamon mixture over the batter.

Pour the remaining batter on top and sprinkle with the remaining cinnamon mixture. Use a knife to swirl the mixture into the batter.

Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted in the center comes out clean.

Allow the cake to cool in the pan for 10 minutes before transferring to a wire rack.

In a small bowl, whisk together powdered sugar, milk, and vanilla extract until smooth.

Drizzle the glaze over the cooled coffee cake before serving.