Preheat oven to 425°F.
Add mozzarella and cream cheese to a large microwave-safe bowl. Melt in the microwave at full power in 30-second intervals. After every 30 seconds, stir cheese until cheese is completely melted and uniform (see photo above). This should take around 1-1 1/2 minutes total. Do not try to microwave the full time at once because some of the cheese will overcook. You can also melt the cheese over the stove in a double boiler.
Add cheese ball to a food processor with the dough blade attachment. Add in almond flour, coconut flour, and egg. Pulse on high speed until the dough is uniform. The dough will be quite sticky, which is normal.
Allow the dough to cool slightly, which will also make it less sticky and easier to work with. Roll the dough out between two sheets of parchment paper until 1/4 inch thick. Peel top sheet of parchment paper off of the dough. Move the dough (still on the bottom parchment paper) onto a baking sheet.
Spread 1/4 cup of mozzarella cheese over the dough, leaving a 1/2 inch perimeter.
Evenly sprinkle the surface of dough with remaining mozzarella cheese and parmesan cheese, leaving a 1/2 inch perimeter. Bake for 3-5 more minutes or until cheese is melted. Garnish with parsley before serving.