In a small bowl, stir together the cream cheese, brown sugar, and cinnamon until smooth and well combined.
Use a rolling pin to flatten each slice of bread. Spread a thin layer of the cream cheese mixture evenly over each slice. Roll the bread up snugly and set aside.
In a shallow bowl, whisk together the eggs, milk, and vanilla.
Dip each roll-up into the egg mixture, coating all sides. Heat butter in a large skillet over medium heat. Cook the roll-ups, turning gently, until golden and crisp on all sides.
Mix powdered sugar and milk in a small bowl until smooth.
Drizzle the glaze over the warm roll-ups and enjoy right away.
