Preheat oven to 350F (175C) and lightly grease the bottom and sides of a 9×13” (23x33cm) metal baking dish (see note if using glass dish).
In a large bowl using an electric mixer, beat together softened cream cheese, softened butter, and sugars until creamy and completely combined.
Add eggs and vanilla extract and stir until completely combined.
In a separate bowl, whisk together flour, baking powder, cornstarch, and salt.
Add about a third of the flour mixture and stir (by hand or with mixer on low-speed) until mostly combined. Then add half of the milk and stir until mostly combined. Repeat until all of the flour and milk have been added and batter is smooth and completely combined.
Spread batter evenly into prepared baking pan and set aside.
Combine melted (but not too hot) butter, brown sugar, and cinnamon and stir together until smooth. Dollop mixture over the surface of your batter and use a knife to swirl throughout the surface of the batter.
Transfer to 350F (175C) oven and bake for 28-32 minutes or until a knife or toothpick inserted in the center comes back clean or with moist crumbs (not wet batter!). Avoid testing directly in the swirl.
While cake cools, prepare vanilla glaze. Note that as the cake cools, the ripple layer will sink into the cake causing brown sugar crevices, this is totally normal and expected!
Whisk together powdered sugar, 1 tablespoon of milk, and vanilla extract, adding additional milk as needed until mixture is smooth and drizzles off the whisk in a ribbon.
Drizzle over warm cake. You can allow the cake to cool completely and the icing to set or you can serve still warm (it will just be a bit messier this way!).