Preheat the oven to 400 degrees F.
Peel and dice the potatoes. Place in a large pot of salted water to cover. Bring to a boil, then simmer until soft, about 15 minutes.
Drain. Transfer to a bowl, add the plant milk, and mash with a fork, a mixer or a food processor -- your choice. Set aside.
While the potatoes are cooking, sauté the onion for a few minutes until soft. Add the garlic, cabbage, and mushrooms, continue to sauté.
Add the lentils and their liquid, the wine, soy sauce, tomato paste, thyme, and pepper. Simmer for 5 minutes.
Dissolve the cornstarch in the cup of broth or water. Add to the lentils. Stir; it will thicken. Add water or broth if it gets too thick.
Lightly oil a 9 x 9 casserole dish. Pour in the lentil mixture, then cover the top with mashed potatoes.
Bake for 15 minutes. Let stand for 10 minutes before serving.