Using a microwave-safe bowl, heat mozzarella cheese in the microwave for a minute, stirring occasionally. Preheat the oven to 350°F.
In a separate bowl, thoroughly mix the coconut flour and almond flour. Add the flour to the melted mozzarella cheese. Once the cheese has cooled, add the egg and mix by hand.
On a flat surface, place a sheet of parchment paper. Add the dough. Lay another piece of parchment paper on top of the dough. Use a rolling pin to flatten the dough between the two pieces of paper.
Remove the top piece of parchment paper. Cut the dough with diagonal lines from the edges to the center, but leave a 4-inch wide space between the cuts. In this center space, alternate layers of ham and cheese. Make at least three layers before topping with chives.
Lay the diagonally cut pieces across the layered ham and cheese one by one until the middle is covered completely.