Whisk the oil, garlic powder, oregano, red pepper flakes, and a pinch each of salt and black pepper in a small bowl.
Whisk the flour, baking powder, and 1/4 teaspoon salt in a medium bowl. Add the yogurt and stir with a fork until crumbly.
Transfer to a work surface and knead with your hands, adding more flour as needed, until it forms a smooth ball (dough should be slightly tacky but not sticky). Cover loosely with plastic wrap; set aside while you grate the cheese and prep the toppings.
Roll the dough into a 12x8-inch rectangle, flouring it and flipping as you go so it doesn’t stick to your work surface.
Brush a thin layer of the seasoned oil onto the dough. Add the sauce in an even layer, leaving a 1/2-inch border. Top with the cheese and any desired toppings. Starting with the SHORT side, carefully roll into a log.
Heat the air fryer to 400°F. Slice the roll into 4 equal pieces with kitchen twine, unflavored dental floss, or a serrated knife. Pinch the seams closed and flatten each roll slightly with the palm of your hand.
Line the air fryer basket with parchment paper and add the rolls. Brush the sides with the remaining oil. Air fry until golden brown and cheese is melted, 7 to 10 minutes. Serve warm.
