Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking dish or line it with parchment paper for easy removal.

In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy. Add the eggs, one at a time, beating thoroughly after each addition. Stir in the vanilla extract.

In a separate bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add the dry mixture to the butter mixture, alternating with the whole milk, beginning and ending with the flour mixture. Stir until just combined, ensuring not to overmix. Pour the batter evenly into the prepared baking dish.

In a medium bowl, combine the melted butter, light brown sugar, all-purpose flour, and ground cinnamon. Stir until smooth and fully incorporated.

Using a spoon, dollop the cinnamon mixture evenly over the cake batter. Using a knife or skewer, gently swirl the mixture through the batter to create a marbled effect.

Place the baking dish in the preheated oven. Bake for 30 to 35 minutes, or until a toothpick inserted into the center of the cake comes out clean. Remove from the oven and allow the cake to cool slightly in the baking dish.

In a small bowl, whisk together the powdered sugar, 2 tablespoons of milk (adding more as needed to reach the desired consistency), and vanilla extract until smooth.

Drizzle the glaze over the warm cake, spreading lightly if desired to ensure even coverage. Allow the glaze to set briefly before slicing and serving.