In a large bowl, stir together the cream cheese, spinach, artichokes, and garlic until well combined. Add the egg, cream, salt, and pepper and mix well. Set aside.
Preheat the oven to 350F and line a rimmed baking sheet with parchment paper. Spread a silicone mat on a work surface and lightly dust with coconut flour.
In a small bowl, whisk together the coconut flour, baking powder, and xanthan gum.
In a large microwave-safe bowl, place the mozzarella. Heat on high in 30 second increments until very melted and can easily be stirred together.
Working quickly, add the flour, then add the egg. Use a rubber spatula to stir together and knead up against the sides of the bowl until cohesive.
Turn the dough out onto the prepared work surface and divide evenly in two. Working with one half at a time, cover with parchment paper and roll out into a circle about 7 to 8 inches in diameter.
Spread half of each circle with half of the filling, leaving a 3/4 inch border. Use an offset spatula or sharp knife to loosen the uncovered half of the dough. Carefully fold over the filling, and pinch the seam together to seal. Place the calzones on the prepared baking sheet.
Brush the tops of the calzones with the melted butter and sprinkle with the sea salt. Use a sharp knife to cut 3 slits into the tops of each.
Bake 25 to 30 minutes, until the calzones are golden brown and the tops are firm to the touch. Remove and let cool 15 minutes before serving.