Cut each refrigerated cinnamon roll into quarters.
Arrange the cut pieces evenly in the prepared baking dish.
In a medium bowl, whisk together 1 cup milk, eggs, and vanilla extract until combined.
Pour the milk mixture evenly over the cinnamon roll pieces.
In a small bowl, mix the granulated sugar and 1/4 teaspoon cinnamon. Sprinkle this mixture over the rolls.
Cover the dish tightly with plastic wrap. Refrigerate for at least 4 hours, or preferably overnight.
When ready to bake, preheat your oven to 350 degrees Fahrenheit. Remove the plastic wrap.
Bake for 30 to 35 minutes, or until the casserole is set and lightly golden brown.
While the casserole bakes, prepare the icing. In a small bowl, beat the softened cream cheese until smooth.
Gradually beat in the powdered sugar and 1 tablespoon milk until the icing is smooth and drizzle-ready.
Remove the casserole from the oven and let it cool for 5 minutes.
Drizzle the cream cheese icing over the warm casserole before serving.
Notes
For a crockpot cinnamon rolls version, place the cut rolls in a slow cooker, pour the custard over, and cook on low for 3-4 hours.
If you need a faster option, you can skip the overnight refrigeration, but let the assembled casserole sit at room temperature for 30 minutes before baking.
This recipe uses canned dough for an easy brunch bake.