In a mixing bowl, combine the rolled oats, milk, honey, vanilla extract, and cinnamon. Whisk until the mixture is smooth and the oats are evenly coated.
Add the brown sugar to the bowl and gently fold it into the oat mixture, creating a light swirl of caramelized sugar within the oats.
Divide the mixture evenly into two small jars or bowls with lids. Cover and place in the refrigerator overnight or at least 4 hours to allow the oats to soak and flavors to meld.
The next morning, open the jars and give the oats a gentle stir to redistribute the cinnamon and sugar swirls. The oats should appear creamy and fragrant, with a visible cinnamon streak.
Serve the cinnamon swirl overnight oats directly from the jar or transfer to a bowl. Optionally, top with fresh fruit, nuts, or a drizzle of honey for added texture and flavor.