In a small bowl, combine 2 tablespoons of granulated sugar with 1 teaspoon of ground cinnamon. Mix well and set aside.

In a shallow dish, whisk together 2 large eggs, 1/4 cup of milk, and 1/2 teaspoon of vanilla extract until smooth.

Flatten each of the 6 slices of bread with a rolling pin. Brush melted butter over one side, then sprinkle with cinnamon sugar. Roll tightly from the buttered side.

Preheat a skillet over medium heat, grease it with butter or oil. Dip each roll-up in the egg mixture and cook seam-side down until golden brown.

Remove roll-ups from the skillet once cooked and serve warm with optional toppings like powdered sugar or fresh fruit.