01 - Preheat oven to 350°F. Line an 8-inch round baking pan with parchment paper or lightly grease it.
02 - Combine shredded mozzarella and cream cheese in a microwave-safe bowl. Microwave in 30-second bursts, stirring until melted and smooth.
03 - Whisk together almond flour, coconut flour, sweetener, baking powder, and salt in a large bowl.
04 - Add the melted cheese mixture and eggs to the dry ingredients. Mix with a spatula until a dough forms. Lightly oil your hands if the dough is sticky.
05 - Place the dough between two sheets of parchment paper. Roll out into a rectangle about 1/4 inch thick.
06 - Mix erythritol, cinnamon, and melted butter. Spread evenly over the dough.
07 - Using the parchment paper to help, gently roll the dough into a log from the long side. Slice into 8 equal pieces.
08 - Arrange the buns cut-side up in the prepared pan. Bake for 22-25 minutes, until golden and set.
09 - Beat together cream cheese, butter, powdered erythritol, and vanilla. Add almond milk as needed for a spreadable consistency.
10 - Remove cinnamon buns from the oven and let cool for 10 minutes. Spread icing over warm buns and serve.