Heat oven to 350°F. Line a rimmed baking sheet with parchment.
Beat cream cheese, powdered sugar, vanilla, milk, and salt until smooth and spreadable.
Trim crusts from the bread and gently flatten each slice with a rolling pin.
Spread 1 to 1½ tablespoons filling over each slice, going nearly to the edges. Roll up tightly.
Stir granulated sugar and cinnamon together in a shallow dish.
Brush each roll-up all over with melted butter.
Roll the buttered logs in cinnamon sugar to coat on all sides.
Arrange seam-side down on the baking sheet. Bake 10–13 minutes, turning once, until crisp and lightly golden.
Cool 5 minutes before serving. Enjoy warm.