In a small microwave-safe bowl, melt 3 tablespoons unsalted butter.
Stir in 3 tablespoons granulated sugar, 2 tablespoons brown sugar, and 1 tablespoon ground cinnamon until smooth to create the filling.
In a shallow bowl, whisk together the eggs and milk to create the custard.
In a separate small bowl, combine 2 tablespoons granulated sugar and 2 teaspoons ground cinnamon for the final coating.
Trim crusts from bread slices and use a rolling pin to flatten each slice to 1/8-inch thickness.
Spread a thin layer of the butter mixture onto each slice and roll up tightly.
Dip each roll into the custard mixture, ensuring it is well coated but not soaked.
Heat 3 tablespoons of butter in a non-stick skillet over medium heat.
Place rolls in the pan seam-side down and cook until golden brown on all sides.
Remove from pan and immediately roll in the cinnamon-sugar coating mixture.
Serve warm with a side of maple syrup.