Prepare the ramekins. Lightly grease 4 to 6 oven-safe ramekins (8 to 10 ounces each) with olive oil or cooking spray.
Set aside.
Sauté aromatics. In a medium saucepan over medium heat, melt butter. Add onion and a pinch of salt. Cook until soft and translucent, 3 to 4 minutes.
Stir in garlic and cook 30 seconds.
Build the roux. Sprinkle in flour and cook, stirring constantly, for 1 minute. This removes the raw flour taste and thickens the sauce later.
Add liquids. Gradually whisk in chicken broth, then milk. Keep whisking to smooth out any lumps.
Simmer 2 to 3 minutes until slightly thickened and silky.
Season and add veggies. Stir in thyme, black pepper, and a pinch of salt. Add frozen mixed veggies and diced potato (if using). Simmer 5 to 7 minutes until the potatoes are just tender.
Fold in chicken. Add cooked chicken and stir to combine.
Taste and adjust seasoning with more salt and pepper as needed. The filling should be creamy but spoonable, not runny. If too thick, splash in more broth; if too thin, simmer a minute longer.
Cool the filling slightly. Remove from heat and let the filling sit for 5 minutes.
Slight cooling helps the crust stay crisp.
Fill ramekins. Divide the filling evenly among the prepared ramekins, leaving 1/4 inch of space at the top.
Top with dough. Roll out pie dough or puff pastry on a lightly floured surface. Cut rounds slightly larger than your ramekins. Drape each round over the filling and crimp or press edges along the rim.
Cut a small slit in the center of each pie for steam to escape.
Egg wash. Brush the tops lightly with egg wash for a glossy, golden finish. Sprinkle with a pinch of salt and pepper if you like.
Preheat the air fryer. Heat your air fryer to 360°F (182°C) for 3 to 5 minutes.
Air fry. Place 2 to 3 pies in the basket, leaving space between them for airflow. Air fry at 360°F for 12 to 16 minutes until the crust is puffed and deep golden and the filling is bubbling at the edges.
Time varies by air fryer and ramekin size.
Rest and serve. Let pies rest for 5 minutes before serving. The filling will set slightly and be easier to eat.