Preheat and prep: Heat your oven to 400°F (200°C). If using puff pastry, let it thaw according to package directions. Lightly grease a 9-inch pie dish or a 2-quart baking dish.
Sauté aromatics: Warm 2 tablespoons of olive oil or vegan butter in a large skillet over medium heat.
Add onion and a pinch of salt. Cook until translucent, about 4–5 minutes. Stir in garlic and cook 30 seconds until fragrant.
Cook the vegetables: Add carrots, celery, potatoes, and mushrooms.
Cook, stirring occasionally, until the mushrooms release moisture and the potatoes start to soften, about 6–8 minutes.
Build the roux: Sprinkle flour over the vegetables and stir to coat. Cook for 1–2 minutes to remove the raw flour taste. If the pan looks dry, add another teaspoon of oil.
Make the sauce: Slowly pour in the vegetable broth while stirring to prevent lumps.
Add plant milk, Dijon, soy sauce/tamari, thyme, bay leaf, and a few grinds of black pepper. Simmer 5–7 minutes, stirring, until thick and creamy.
Finish the filling: Stir in peas, corn, greens, and optional chickpeas or white beans. Simmer 2–3 minutes until the greens wilt.
Remove the bay leaf. Adjust salt and pepper. Stir in parsley.
Assemble: Transfer the filling to your baking dish.
Lay puff pastry or pie dough over the top. Trim or tuck edges as needed. Cut a few small slits for steam to escape.
For extra color, brush the crust with a little plant milk or olive oil.
Bake: Place on a sheet pan to catch drips. Bake 25–35 minutes until the crust is golden and the filling is bubbly around the edges.
Rest and serve: Let the pot pie rest 10–15 minutes before slicing. This helps the filling set and makes serving easier.