Instructions

Flatten each piece of white bread using a rolling pin.
Whisk 1/4 cup butter, sugar, and cinnamon together in a bowl. Whisk eggs, milk, and nutmeg together in a separate bowl.
Spread cinnamon butter mixture onto 1 side of each piece bread. Roll bread around the cinnamon butter. Dip rolled bread into the egg mixture.
Melt 2 tablespoons butter in a skillet over medium heat; cook the dipped bread rolls until golden, about 2 minutes per side.