Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large bowl, combine flour, baking powder, salt, and sugar. Add eggs, milk, melted butter, and vanilla extract. Mix until smooth.
Pour the batter into the prepared baking dish, spreading it evenly.
In a separate bowl, mix brown sugar and cinnamon for the swirl. Drop spoonfuls of softened butter over the batter and sprinkle the cinnamon sugar mixture over the top. Use a knife to swirl it into the batter.
Bake for 30 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, make the glaze by whisking together powdered sugar, milk, and vanilla extract.
Let the cake cool for 10 minutes, then drizzle the glaze over the top.
Slice, serve, and enjoy!