Prepare the potatoes: Chop them into small pieces. Cover with water in a pot and bring to a boil, then turn heat down and simmer 10 to 15 minutes until you can stick a fork easily through the potatoes. Drain the potatoes, then mash them straight in the pot, adding the plant milk, margarine, salt and pepper. Keep mashing until smooth. Taste for salt and pepper and adjust as needed.
Prepare the filling: Heat the olive oil in a large pan over medium-high heat. Add the onion and carrots/parsnips/beets and cook until they begin to brown a bit, about 5-6 minutes. Add the garlic, then the plant-based ground meat, salt and pepper and stir until browned and cooked through, about. 3 minutes. Sprinkle the brown rice flour in and stir to coat, then cook for another minute. Add the broth, tamari, and oregano, and stir to combine. Bring to a boil, reduce the heat to low, cover and simmer for 5-10 minutes until the sauce has thickened a bit.
Add the peas and/or corn to the mixture, then spread evenly into an 11 x 7-inch glass baking dish. Top with a smooth layer of the mashed potatoes, creating a seal around the edges to prevent the mixture from bubbling up.
Bake at 400F for 25 minutes or until the potatoes begin to brown. Remove and cool for at least 15 minutes before serving.