01 - Preheat oven to 350°F. Line an 8-inch round baking pan with parchment paper or lightly grease with butter.
02 - Combine shredded mozzarella and cream cheese in a microwave-safe bowl. Microwave in 30-second intervals, stirring between each, until completely melted and smooth.
03 - In a large mixing bowl, whisk together almond flour, coconut flour, erythritol, baking powder, and salt until well incorporated.
04 - Add the melted cheese mixture and eggs to the dry ingredients. Mix thoroughly with a spatula until a cohesive, sticky dough forms. Lightly oil hands to handle dough if necessary.
05 - Place dough between two sheets of parchment paper. Roll into a rectangle approximately 1/4 inch thick, ensuring even thickness throughout.
06 - In a small bowl, mix erythritol, ground cinnamon, and melted butter until combined. Spread evenly over the rolled dough surface.
07 - Use the parchment paper to lift and roll the dough into a tight log from the long edge. Cut into 8 equal portions using a sharp knife or unflavored dental floss.
08 - Arrange buns cut-side up in the prepared pan. Bake for 22 to 25 minutes until golden brown and set in the center.
09 - While buns bake, beat softened cream cheese, butter, powdered erythritol, and vanilla extract until smooth and creamy. Add almond milk 1 tablespoon at a time until spreadable consistency is reached.
10 - Remove buns from oven and let cool for 10 minutes. Spread prepared icing generously over warm buns and serve immediately.