Preheat the oven to 350°F (175°C) and grease the 9x13 inch baking pan.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add in the eggs, vanilla extract, and milk, then mix until well combined.
In another bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.
In a small bowl, combine the brown sugar and ground cinnamon for the filling.
Pour half of the cake batter into the prepared pan. Sprinkle the cinnamon-sugar mixture evenly on top, followed by the remaining cake batter.
Using a knife or toothpick, swirl the batter gently to create a marbled effect.
Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
While the cake is baking, prepare the glaze by whisking together the powdered sugar, milk, and vanilla extract until smooth.
Once the cake is done, allow it to cool in the pan for about 10 minutes, then drizzle the glaze on top before serving.