Add the olive oil and diced onions to a pan and sauté on medium heat until very lightly caramelized.
Using the shredding attachment of a food processor, shred the potatoes and parsnip and add to a large mixing bowl. Fold in the sautéed onion, eggs, matzo meal, parsley, salt, pepper and half the cheese.
Pour the mixture into a casserole dish (approx. 10”) and top with the remaining cheese. Bake for 1 hour and serve warm.