In a food processor, combine the flour and salt and pulse 3-4 times. Add the cold butter cubes and process until the mixture is crumbly.
In a medium bowl, combine the yogurt, water, and lemon juice. Slowly add the liquid to the flour mixture with the food processor running until the dough comes together.
Turn the dough out onto a floured work surface and shape it into a disk. Cover with plastic wrap and place in the refrigerator for at least 1 hour. (Don’t skip this step!)
Chop apples and place them into a medium saucepan along with the cinnamon and sugar. Stir to combine. Cook over medium heat for 8 minutes or until the apples release their juices and become tender. Remove from heat and allow to cool while the pie dough chills.
Preheat the air fryer to 350 degrees F. Spray the basket with olive oil spray.
Unwrap the dough and roll it out to about 1/4-inch thick. Using a medium bowl, cut circles from the dough. Re-roll the dough scraps and cut until you have 8 dough circles. (This is a soft dough, but the yogurt makes it easy to work with.)
In the middle of the circles, place 1-2 tablespoons of the apple mixture. Fold one-half of the circle over to match the opposite edge to enclose the pie filling. Use a little water brushed onto the edges of the dough to help seal the edges. I like to crimpy the edges with the tines of a fork too.
In a small bowl, beat together the egg and water. Then brush onto the tops of the hand pies with the egg wash and sprinkle with coarse sugar. Cut 3 slits into the tops of the pies.
Place pies in the air fryer basket. (Do not crowd, you'll need to cook in batches). Cook for 10-15 minutes until the pies are golden brown.
Remove the pies from the basket and repeat with the remaining pies. Serve warm with caramel sauce, if desried.
Notes
The pie dough can be made ahead of time and chilled until ready to make the pies.