Place the carrots and parsnips in a medium to large pot and cover with cold water. Set on the stove, bring to a simmer, and cook until very tender, about 15 minutes. Drain well and place the carrots and parsnips in a food processor. Add the remaining ingredients, except garnish, and pulse until smooth.
Spoon the dip into a bowl, cool to temperature and refrigerate until chilled. When ready to serve, garnish the dip, if desired, with a drizzle of olive oil and a few walnuts pieces.