Plug in a mini waffle maker and let it preheat fully. In a small bowl, mix together the granulated erythritol and ground cinnamon for the coating. Set aside.
In a medium bowl, whisk the egg, then stir in the shredded mozzarella, almond flour, softened cream cheese, and vanilla extract until you have a smooth, well-combined batter.
Lightly grease the waffle maker with a tiny bit of cooking spray. Spoon about 2 tablespoons of batter into the center and close the lid. Cook for 3 to 4 minutes, or until the chaffle is golden and crisp. Repeat with the remaining batter to make about 4 chaffles.
As soon as each chaffle comes out of the waffle maker, brush both sides generously with melted butter using a pastry brush.
Immediately press the buttered chaffle into the cinnamon erythritol mixture, coating both sides evenly. The warmth of the chaffle helps the coating stick perfectly.
Serve the churro chaffles warm. They are best enjoyed right away when the outside is crispy and the center is soft.