In a small bowl, mix the softened cream cheese, powdered sugar, and vanilla extract until smooth and creamy. Set aside.
In a separate shallow dish, combine the granulated sugar and ground cinnamon. Set aside for coating the roll-ups.
Flatten each bread slice with a rolling pin until thin and pliable. Spread about 1 tablespoon of the cream cheese mixture evenly over one side of each bread slice.
Roll up each bread slice tightly, starting from one end, to form a cylinder. Press gently to seal the edge.
In a shallow bowl, whisk together the beaten eggs and milk. Dip each bread roll-up into the egg mixture, coating it evenly on all sides.
Heat a large nonstick skillet over medium heat and add 1 tablespoon of unsalted butter. Place 4 roll-ups in the skillet and cook for 1-2 minutes per side, or until golden brown. Repeat with the remaining roll-ups, adding more butter as needed.
Immediately roll the cooked roll-ups in the cinnamon-sugar mixture until fully coated. Dust with additional powdered sugar before serving.