Set the Instant Pot to Sauté – More/High. Add olive oil, onions, and garlic, and cook until translucent, about 2-3 minutes. Add the carrots, celery, peas, rosemary, thyme, and parsley. Sauté for 5 minutes, or until the vegetables are slightly softened.
Stir in the flour, salt, and pepper, and cook for 1 minute to remove the raw taste of the flour. Gradually whisk in the chicken broth and milk, stirring constantly until the mixture thickens into a creamy sauce. Add the shredded turkey and stir to combine. Adjust seasoning to taste. Turn off the Instant Pot and allow the filling to cool slightly.
Roll out the pie crusts and use the rim of a Pyrex 6-ounce custard cup as a guide to cut circles slightly larger than the rim. Cut out enough circles for both the bottoms and tops of the pies (12 total).
Line the bottom of each custard cup with a circle of pie crust, pressing it into the edges. Fill each cup with about ¾ cup of the turkey filling. Cover with a top crust, sealing the edges by pinching or crimping. Cut small slashes in the top crust to allow steam to escape. Repeat for all six custard cups.
Brush the tops of the pies with beaten egg. Preheat the air fryer on the Bake function to 360°F (180°C). Place as many custard cups as will fit into the air fryer and bake for 15 -17 minutes, or until the crust is golden brown and crisp. Repeat the process until all pies are baked.
Let the pot pies cool for 5 minutes before serving. Serve warm and enjoy the perfect balance of flaky crust and creamy filling.