Heat one tablespoon of the butter and the olive oil over medium-high heat in a large Dutch oven or saucepan. Add the onion, season lightly with salt, and stir until evenly coated with the butter.
Lower the heat and cook for 15-20 minutes, or until the onions are soft, golden brown and slightly caramelized.
Add the carrot, parsnip, sweet potato and butternut squash. Cook until softened about 8 minutes. Transfer the vegetables to a clean bowl and wipe the pot clean (don’t worry about any browned bits that may stick – they will add flavour to the sauce).
Return the Dutch oven to the stove and melt the remaining butter over medium-low heat. Add the flour and stir until well combined, cooking for at least two minutes. Slowly stir in the broth, whisking as you go. Scrape any browned bits from the bottom of the pot.
Bring the liquid to a boil, then lower the heat and simmer until the sauce has thickened slightly. Check the seasonings and adjust the salt and pepper if needed. Add the cooked vegetables, peas, parsley and thyme to the pot and stir well.
Preheat the oven to 375 degrees. Divide the filling evenly between four ovenproof soup bowls. Set the bowls on a baking sheet lined with aluminum foil. Divide the pie crust into four equal portions and roll each piece into a 6” circle.
Brush the outside edges of each bowl with the egg wash, then place the pastry on top. Trim the circle to 1/2” larger than the top of the bowl, and fold over the underside of the dough, pressing it to the bowl to make it stick.
Brush the dough with the egg wash and make three slits in the top. Place the pies on the prepared baking sheet and bake for 40 minutes, or until the top is golden brown and the filling is heated through.
The filling can be made up to two days in advance and stored in the fridge in a little container. The dough can also be made up to two days in advance, if storing in the fridge, or six months ahead if storing in the freezer.