Begin by removing the crusts from each slice of white sandwich bread. Use a rolling pin to flatten each slice gently, taking care not to tear the bread.

In a small bowl, mix together the melted butter, brown sugar, and 2 tablespoons of cinnamon until well combined. Spread this mixture evenly over each flattened bread slice.

Starting from one end of each slice, roll the bread tightly into a cylindrical shape and seal the edges.

In a shallow bowl, whisk together the large eggs, milk, ½ teaspoon of cinnamon, and vanilla extract until smooth.

Place a non-stick skillet over medium heat and add a small amount of butter to coat the bottom of the pan.

Dip each rolled-up slice into the egg mixture, ensuring that it is well-coated but not overly soaked. Cook for about 2-3 minutes, turning occasionally, until golden brown on all sides.

Once cooked, remove the roll-ups from the skillet and transfer them to a warm plate. Serve warm.