Wash and peel the potatoes, and cut them into quarters. Add them into a large pot, and cover with water. Add some salt, cover with a lid and bring to a low boil. Cook the potatoes until tender but still firm, about 15 to 20 minutes; drain.
While the potatoes are cooking, rinse the lentils, and drain well. Transfer them into a medium-size pot or saucepan; add 2 cups of vegetable broth, 1 cup of water, a pinch of salt, and bay leaves. Bring to a low boil, cover with a lid, reduce heat and simmer until they are tender (typically 15-20 minutes).
In the meantime, preheat the oven to 425°F (220°C). And prepare a 2-quart baking dish (9 x 13-inch casserole also works).
In a large non-stick pan or pot, heat ¼ cup of vegetable broth and sauté the onion. Add the mushrooms, and cook them with the onion for about 7 minutes. Drain the lentils, and add them to the preparation. Add the tomato paste, paprika, cumin, coconut aminos, salt, and pepper to taste, and mix well. Remove from the heat, add the olives and stir to combine. Reserve.
Drain the potatoes using a colander. Return them to the pot, and mash them with a potato masher. Add salt, pepper, nutmeg, and plant-based milk, and stir until smooth.
Add the lentils and mushrooms into the baking dish, filling an even layer. Finally, carefully top with the mashed potatoes. Spread gently, and smooth down.
Bake the shepherd’s pie for 25 minutes, and then broil it for about 5 minutes (watching it all the time, so it doesn’t burn), or until the top is lightly golden brown and the dish bubbles.
Remove from the oven, let it cool a little (it’ll thicken as it cools), and enjoy!