Start by preheating your oven to 425°F so it's fully hot by the time your filling is ready. Lightly spray six 4-inch ramekins or small oven-safe pots with nonstick spray so nothing sticks later. Set them aside on your counter while you build the filling.
Melt the butter in a large skillet over medium heat, then add the chopped onion, carrots, and celery. Cook for about 5 minutes, stirring occasionally, until the onion turns soft and translucent. This step builds the flavor foundation for the entire filling.
Stir in the sliced mushrooms and minced garlic, cooking for another 3 minutes or so. You want the mushrooms tender and any liquid they release to cook off completely. Keep stirring so the garlic doesn't scorch and turn bitter.
Sprinkle the flour directly over the vegetables and stir until everything is evenly coated. Slowly pour in the chicken broth and heavy cream while whisking to prevent lumps. Let it simmer for 3 to 4 minutes until the mixture thickens into a rich gravy.
Stir in the thyme, salt, and black pepper to season the gravy to your taste. Add the cooked chicken, frozen peas, and fresh parsley, folding everything together gently. Remove the skillet from the heat and let the filling cool slightly before assembling.
While the filling cools, roll out your pie crust and cut six circles about 4¼ inches wide for the bottoms. Press one circle into each prepared ramekin so it lines the bottom snugly. Use the leftover dough scraps to cut thin strips for the mummy bandages.
Spoon the cooled filling into each lined ramekin until it's nearly full to the top. Lay the dough strips across each pie in a crisscrossed, overlapping pattern like mummy wrappings. Leave a small gap between a couple of strips so the candy eyes can peek through later.
Whisk the egg with a teaspoon of cold water and brush it generously over the dough strips. Place the ramekins on a baking sheet, then bake for 20 to 25 minutes until deeply golden and bubbling. Let them cool for a few minutes before pressing the candy eyes into the gaps to finish the mummy look.