Combine flour, salt, sugar, and yeast in a large bowl.
Make a well, add warm water and olive oil, stir until dough forms.
Knead dough on floured surface for 8–10 minutes until smooth and elastic.
Place dough in oiled bowl, cover, and let rise 1–1.5 hours until doubled.
Prepare fillings by combining cooked turkey bacon, chicken ham, bell peppers, mushrooms, mozzarella, garlic powder, and oregano.
Punch down dough and divide into 6 portions; roll each into a 6-inch circle.
Place filling on half of each dough circle, fold over, and seal edges by crimping with a fork.
Brush tops with beaten egg.
Preheat air fryer to 375°F (190°C) for 3–5 minutes.
Air fry 2–3 calzones at a time for 12–15 minutes until golden brown, flipping if needed.
Let cool slightly and serve with your favorite dipping sauce.