Heat oven to 350°F. Grease a 9x13-inch pan or line with parchment.
Whisk flour, sugar, baking powder, and salt in a large mixing bowl.
Add milk, beaten eggs, vanilla, and melted butter. Mix until just smooth.
Spread the batter evenly into the prepared pan.
Combine brown sugar, cinnamon, softened butter, and a pinch of salt into a paste.
Spoon dollops over the batter. Swirl with a knife to create ribbons.
Bake 32 to 38 minutes, until golden and a tester comes out clean.
Cool the cake 10 minutes while you prepare the glaze.
Beat cream cheese, powdered sugar, vanilla, and milk until smooth and pourable.
Drizzle glaze over the warm cake. Slice and serve.