Peel the potatoes and parsnips, then cut them into evenly sized pieces to ensure uniform cooking.
Place the cut vegetables in a large pot and cover them with cold water. Bring to a boil, then reduce the heat and simmer until the vegetables are tender, about 15-20 minutes.
Drain the vegetables. Then, put them back in the same pot (after having emptied the water and quickly wiped it dry) and turn the heat to low.
Mash the vegetables with a potato masher until smooth.
Incorporate the margarine or oil, then gradually add the plant-based milk while mixing, until the desired consistency is achieved.
Season with salt, white pepper, and nutmeg. Taste and adjust the seasoning if necessary.
Serve the mash hot, garnished with fresh chopped parsley if desired.