Boil potatoes in a pot with water and salt. Once soft, drain and mash them using a potato masher or hand mixer.
Preheat the oven to 400°F (200°C).
In a large pan, heat some oil over medium heat. Add the onion and garlic, and cook until softened, about 5 minutes.
Add the plant-based ground beef to the pan and cook until browned, about 5 minutes.
Stir in the dried thyme, oregano, salt, pepper, tomato sauce, and green beans. Simmer until the vegetables are tender and the sauce has thickened, about 10 minutes.
Grease a 9-inch pie dish and spread the filling evenly across the bottom. Cover with a thick layer of mashed potatoes.
Bake the pie in the oven for 25-30 minutes, or until the crust is golden brown.
With the help of a towel or oven gloves, remove the casserole from the oven, sprinkle the cheese over the potato and put the casserole back in for another 7-10 minutes.
Serve hot, garnished with fresh parsley and with a side salad or steamed vegetables, if desired.