Heat the oven to 350°F and line a baking sheet with parchment.
Stir the softened cream cheese, powdered erythritol, and vanilla until smooth.
Flatten each bread slice with a rolling pin, keeping the slices intact.
Spread the cream cheese mixture over the bread and roll each slice tightly from one end.
Dip each roll in beaten egg, turning to coat all sides.
Arrange the rolls seam-side down on the prepared sheet and brush with melted butter.
Mix the granulated erythritol and cinnamon, then sprinkle the mixture over the rolls.
Bake for 12 to 15 minutes, turning once if needed, until golden and crisp. Cool briefly before serving.