Preheat and prep. Heat your oven to 400°F (200°C). Lightly oil a 9x13-inch baking dish or similar casserole.

Cook the potatoes. Add peeled, cubed potatoes to a pot of salted cold water. Bring to a boil and cook until very tender, 12–15 minutes. Drain well and return to the hot pot to steam off excess moisture.

Make the mashed topping. Mash potatoes with vegan butter or olive oil, warm plant milk, salt, and pepper. Aim for a smooth but spreadable texture. Taste and adjust seasoning. Set aside.

Sauté the aromatics. In a large skillet or Dutch oven, warm 2 tablespoons olive oil over medium heat. Add onion, carrot, and celery. Cook until softened, 6–8 minutes. Stir in garlic and cook 1 minute more.

Add mushrooms and seasonings. Stir in chopped mushrooms with a pinch of salt. Cook until they release their moisture and brown slightly, 5–7 minutes. Add thyme, rosemary, and smoked paprika if using.

Build the sauce. Stir in tomato paste and cook for 1–2 minutes to caramelize. Sprinkle flour over the mixture and stir for 1 minute. Pour in vegetable stock, soy sauce, and vinegar, whisking to avoid lumps. Bring to a gentle simmer.

Cook the lentils. Add rinsed lentils to the pan. Simmer uncovered, stirring occasionally, until lentils are tender but not mushy, 25–30 minutes. Add a splash of stock or water if it gets too thick.

Finish the filling. Stir in peas and corn. Taste and adjust salt and pepper. The filling should be saucy but not soupy; it will thicken slightly in the oven.

Assemble the pie. Transfer the lentil mixture to your baking dish and smooth it out. Spoon the mashed potatoes on top in dollops, then spread gently to cover. Use a fork to make ridges for extra browning.

Bake. Place the dish on a sheet pan to catch any bubbles. Bake 20–25 minutes, until the top is lightly golden and the filling is bubbling at the edges. For deeper color, broil for 1–3 minutes, watching closely.

Rest and serve. Let the pie rest 10–15 minutes to set. Sprinkle with chopped parsley and serve warm.