Preheat the oven to 400°F. Lightly grease a 9-inch by 13-inch baking pan and set aside.
Start by making the mashed potatoes. Place the peeled and diced potatoes in a medium-large saucepan and cover with cold water. Bring to a boil over high heat, add a generous pinch of salt, and cook for 10 to15 minutes, until the potatoes are very soft when pressed against the side of the pot. Drain the potatoes, transfer to a bowl, and add the vegan butter, salt, and pepper. Mash with a potato masher until mostly smooth, then add the non-dairy milk and continue to mash until the desired texture is reached. Cover the bowl with plastic wrap to keep warm, and set aside.
While the potatoes are cooking, begin the stew. Place the dried porcinis and vegetable stock in a medium saucepan, bring to a boil, then remove from the heat and cover until needed. Meanwhile, heat the olive oil in a large, deep sauté pan or Dutch oven over medium-high heat. Add the onion and a pinch of salt, and sauté until translucent, about 7to 10 minutes. Add in the garlic, carrots, rutabaga, celeriac, and mushrooms, and cook until the mushrooms have released their liquid and the other vegetables are beginning to soften, about 5 minutes more. While the vegetables are cooking, strain the rehydrated porcinis from the mushroom stock, reserving the stock, and roughly chop the mushrooms. Add the porcinis, thyme, and tomato paste to the vegetables, and cook for an additional minute or two. Pour in the wine and allow it to reduce slightly, then add the reserved mushroom stock and salt. Bring to a boil, cover the pot, then reduce the heat and allow it to simmer for 20 minutes. Stir in the cooked lentils.
Combine the flour and water in a small bowl, and whisk together until smooth. Pour into the stew, stirring well, and continue to stir until the stew is slightly thickened, which will take approximately 5 minutes. Taste the stew and adjust seasonings as necessary.
Pour the hot stew into the lightly oiled pan, then spoon or pipe the mashed potatoes evenly over the top. Place the pan on a sheet tray, then transfer carefully to the oven. Bake for 20 to 30 minutes, until the stew is bubbling and the potato topping is just starting to brown. Allow to cool slightly, then serve hot. Leftovers can be refrigerated for 5 to 7 days, or frozen for up to 3 months.
