Prepare the pie crust: In a large bowl, whisk together 330g (2.5 cups) all-purpose flour and 1 tsp (5g) salt. Add 225g (1 cup) cold, cubed unsalted butter. Using a pastry blender, your fingertips, or a food processor, cut the butter into the flour until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining. This is crucial for a flaky crust.

Gradually add 120-180ml (0.5-0.75 cup) of ice water, one tablespoon at a time, mixing until the dough just comes together. Be careful not to overmix. Press the dough into a ball, divide it in half, flatten each half into a disc, wrap in plastic wrap, and refrigeritate for at least 30 minutes (or up to 2 days).

Preheat your oven to 200°C (400°F). While the dough chills, begin preparing the vegetable filling. Heat 30ml (2 tbsp) olive oil in a large oven-safe skillet or Dutch oven over medium heat.

Add the chopped onion, diced carrots, and diced celery to the skillet. Sauté for about 5-7 minutes, or until the vegetables begin to soften. Add the diced potatoes and cook for another 5 minutes, stirring occasionally.

Stir in the sliced mushrooms and minced garlic. Cook for an additional 5-7 minutes, until the mushrooms have released their liquid and started to brown.

In a separate small saucepan, melt 50g (4 tbsp) of unsalted butter over medium heat. Whisk in 50g (6 tbsp) of all-purpose flour and cook for 1-2 minutes, whisking constantly, to create a roux. Do not let the roux brown.

Gradually whisk in 500ml (2 cups) of vegetable broth, followed by 250ml (1 cup) of milk. Continue whisking until the sauce is smooth and begins to thicken. Bring it to a gentle simmer.

Pour the thickened gravy mixture into the skillet with the vegetables. Stir in the frozen peas, frozen corn, 1 tbsp (approx. 3g) fresh thyme leaves, 2 tbsp (approx. 6g) chopped fresh parsley, 1.5 tsp (9g) salt, and 0.5 tsp (2g) black pepper. Stir well to combine all ingredients.

Remove the skillet from the heat. On a lightly floured surface, roll out one disc of chilled pie dough into a circle large enough to cover the top of your skillet (approximately 25-30cm / 10-12 inches in diameter).

Carefully place the rolled-out dough over the vegetable filling. Trim any excess dough, leaving about a 1.5cm (0.5 inch) overhang. Crimp the edges of the dough to the rim of the skillet to seal. Cut a few vents in the top crust to allow steam to escape.

Brush the top crust evenly with the beaten egg wash. This will give the crust a beautiful golden-brown color and shine.

Place the skillet on a baking sheet (to catch any drips) and bake in the preheated oven at 200°C (400°F) for 20 minutes. This initial high heat helps the crust to puff up and become golden.

Reduce the oven temperature to 180°C (350°F) and continue baking for another 25-30 minutes, or until the crust is deeply golden brown and the filling is bubbling hot. If the crust starts to brown too quickly, you can loosely tent it with aluminum foil.

Once baked, carefully remove the pot pie casserole from the oven. Let it rest for at least 10-15 minutes before serving. This allows the filling to set slightly and makes it easier to serve.