Preheat oven to 350°F (175°C). Grease a 9×5-inch loaf pan.
Whisk flour, granulated sugar, baking powder, and salt in a large bowl.
In another bowl, whisk together milk, eggs, melted butter, and vanilla.
Add the wet ingredients to the dry ingredients and stir just until combined.
Mix brown sugar, cinnamon, and melted butter in a small bowl.
Pour half of the batter into the loaf pan.
Add half of the cinnamon mixture, followed by the remaining batter and remaining cinnamon mixture.
Gently swirl with a knife or skewer.
Bake for 45–55 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs.
Cool in the pan for 10–15 minutes, then transfer to a wire rack.
Whisk powdered sugar, milk, and vanilla until smooth.
Drizzle icing over the slightly warm bread.
Slice and serve.