Preheat oven to 425 degrees F. Line two baking sheets with parchment paper, set aside.
Place a large skillet over high heat with the oil. Once hot, add the chicken and cook until evenly browned and crispy, about 8 to 10 minutes. Stir in the onions and garlic. Cook until softened, about 2 to 3 minutes more. Add the spinach, a handful at a time, and cook until the spinach has wilted. Stir in the artichoke and sun-dried tomatoes. Season with salt, pepper, oregano, and crushed red pepper flakes. Cook for a minute or two longer. Remove from heat and let cool for about 10 to 15 minutes. Stir in the mozzarella and feta cheese.
Cut each pizza dough into fourths and then working with one piece at a time, roll each into a thin circle, about 1/4 of an inch thick. Fill one side with a few heaping tablespoons of the filling. Fold over to create half a moon shape and then crimp the edges to seal and make sure the filling doesn't come out during baking. Place on the prepared baking sheets, continuing to fill and fold the remaining calzones. Brush each with the egg wash and bake until evenly browned, about 20 to 25 minutes. Remove from oven and let cool slightly before serving.
Meanwhile, make the tzatziki. In a large bowl, combine the yogurt, cucumbers, lemon zest and juice, garlic, parsley, sill, salt and pepper. Stir until evenly combined. Give it a taste and adjust seasonings accordingly, adding more salt or pepper as needed. Cover with plastic wrap and let chill in fridge until ready to use. Can be made up to 4 days in advance, and stored in the fridge in an airtight container.
Serve the calzones with the tzatziki sauce on top. Calzones can be baked, cooled and frozen for up to 3 months. Just rewarm in a preheated 350 degree oven for about 10 to 15 minutes. Enjoy!