Preheat your oven to 375° and place 8 ramekins onto a rimmed metal baking sheet.
Melt 3 tablespoons of butter in a large Dutch oven over medium to medium-low heat.
Add in the diced carrots, celery and onon with a pinch of salt and cook for 10 to 12 minutes.
Now add in the remaining butter and the thyme. Stir and cook for a minute.
Next add in the flour, stirring often while it cooks for 2 minutes.
Pour in the 3 cups of chicken broth and 1-1/2 cups of whole milk. Let that simmer, stirring occasionally until thickened. About 15 minutes.
Once thickened, remove the pot off of the heat and add in the diced cooked chicken, frozen peas, corn and parsley. Stir. Taste and season with salt and black pepper, to taste. Allow this to cool.
Meanwhile, evenly divide some of the diced cooked potatoes into each ramekin.
Ladle the pot pie filling evenly over the potatoes, dividing it evenly among all the ramekins. Make sure the filling has cooled significanlty before placing the pie dough over top and crimping the edges. Use a sharp knife make slits for ventilation.
Brush with an egg wash*, if desired.
Slide the sheet pan onto the middle rack of your preheated oven and bake for 30 minutes or until the crust is golden and the filling is bubbling.
Remove and let them cool for 10 minutes before serving.