Preheat oven to 350°F (175°C) and grease an 8x8-inch square baking pan with butter or non-stick spray.
In a large mixing bowl, whisk together the rolled oats, 1/2 cup brown sugar, baking powder, 1 teaspoon cinnamon, and sea salt.
In a separate medium bowl, whisk together 2 cups milk, eggs, 2 tablespoons melted butter, and vanilla extract until homogenous.
Pour the liquid mixture over the dry ingredients and stir with a spatula until the oats are thoroughly hydrated.
Transfer the oat mixture into the prepared baking pan, spreading it into an even layer.
In a small bowl, prepare the swirl by mixing 1/4 cup brown sugar, 1 tablespoon cinnamon, and 2 tablespoons melted butter until it forms a paste.
Drop small dollops of the cinnamon paste onto the surface of the oats and use a butter knife to swirl the mixture into the top layer of the oatmeal.
Bake for 30 to 35 minutes, or until the oatmeal is set in the center and the edges are slightly golden brown.
While the oatmeal cools slightly, whisk the softened cream cheese, powdered sugar, and 1 tablespoon milk until a smooth, pourable glaze forms.
Drizzle the glaze over the warm oatmeal squares and slice into 9 equal portions for service.