Heat the oven to 350°F (175°C) and grease a 9x13-inch baking dish.
In a large bowl, whisk together flour, sugar, baking powder, and salt. Add milk, eggs, vanilla, and melted butter, then mix until smooth. Pour the batter into the greased dish.
In a separate bowl, mix softened butter, brown sugar, and cinnamon until thick and spreadable.
Swirl into the batter: Drop spoonfuls of the cinnamon mixture over the cake batter. Use a knife or toothpick to swirl it through, creating a marbled effect.
Bake: Place the dish in the oven and bake for 35-40 minutes until a toothpick inserted in the center comes out clean.
Make the glaze: While the cake bakes, whisk powdered sugar, milk, and vanilla until smooth.
Glaze and serve: Drizzle the glaze over the warm cake. Let it sit for a few minutes before slicing and serving.