Preheat oven to 350°F (175°C) and grease your bundt pan thoroughly.
In a bowl, whisk together the flour, baking powder, and salt; set aside.
Cream butter and granulated sugar in a large bowl until light and fluffy.
Add eggs one at a time, beating well after each addition, then mix in vanilla extract.
Alternately add the dry ingredients and milk to the butter mixture, beginning and ending with dry ingredients. Mix until just combined.
In a separate small bowl, combine brown sugar, cinnamon, and melted butter to make the cinnamon swirl mixture.
Pour half of the batter into the bundt pan, then sprinkle half of the cinnamon swirl over it.
Add remaining batter, then top with remaining cinnamon swirl mixture.
Use a knife or skewer to gently swirl the cinnamon mixture through the batter for a marbled effect.
Bake for 50-60 minutes, or until a toothpick inserted in the center comes out clean.
Allow cake to cool in the pan for 10 minutes, then turn out onto a wire rack to cool completely.
To make the glaze, whisk powdered sugar, milk, and vanilla extract until smooth and drizzle over the cooled cake.