Make cinnamon butter and bread: In a bowl, mix butter, light brown sugar, and cinnamon until well combined. Cut the crusts off the bread, then use a rolling pin to roll the slices flat. Spread the cinnamon butter mixture over each slice, then roll them up tightly.
Create your French toast: In a separate bowl, whisk together the eggs, milk, and vanilla extract. Dip each bread roll in the egg mixture, ensuring it’s completely coated. Melt the additional butter in a skillet over medium heat, then fry the rolls until golden brown on all sides.
Make the coating and icing: Mix granulated sugar and cinnamon in a small bowl. Roll the cooked French toast rolls in the sugar-cinnamon mixture to coat them evenly. For the icing, blend together the softened butter, cream cheese, and confectioners’ sugar until smooth. Use the icing as a drizzle over the rolls or as a dip.