Preheat oven to 350°F (175°C) and grease a 9x13-inch baking dish. In a mixing bowl, whisk together flour, sugar, baking powder, and salt. Add milk, eggs, vanilla, and melted butter, stirring until smooth.
In a separate bowl, mix softened butter, brown sugar, cinnamon, and flour until well combined. Drop spoonfuls of the mixture over the batter, then swirl it in with a knife for a marbled effect.
Pour the batter into the greased baking dish and bake for 35 minutes, or until a toothpick inserted in the center comes out clean.
While the cake is warm, whisk together powdered sugar, milk, and vanilla for the glaze. Drizzle over the cake and let it set for a few minutes before serving.