Start by removing the crusts from each slice of white sandwich bread. Using a rolling pin, flatten each slice gently until it's about ¼ inch thick.

In a small bowl, combine the melted butter, brown sugar, and 2 tablespoons of ground cinnamon until well mixed. Spread the mixture evenly over each flattened bread slice.

Carefully roll each slice of bread tightly from one end to the other, ensuring the filling stays inside. Press the edges to seal them.

In a shallow bowl, whisk together the eggs, 1 tablespoon of milk, the remaining ½ teaspoon of cinnamon, and vanilla extract until well combined.

Preheat a non-stick skillet over medium heat and add 2-3 tablespoons of butter until melted.

Take each roll-up and dip it into the egg mixture, ensuring it's coated lightly on all sides. Place each roll seam-side down into the skillet.

Cook for about 2-3 minutes, rotating them gently until they’re golden brown on all sides.

Remove the roll-ups from the skillet and place them on a serving platter. Sprinkle with cinnamon sugar if desired.