Fill a large pot with salted water, add the potatoes and carrots, and bring to a boil. Cover and cook for about 30 minutes or until tender. Remove from the pot and let cool.
Fill another small pot with salted water and add the peas, bring to a boil, and cook until the peas are tender, about 5 minutes. Remove from the pot and reserve.
When the potatoes are warm to the touch, peel them with your hands. In a large mixing bowl, mash the potatoes with a masher until all of the potatoes are completely mashed.
One by one, mix in the peas, carrots, mayonnaise, sour cream , mustard, onion, parsley, eggs, nutmeg, and pepper until well combined.
Butter a 3.8 L baking dish and spread the potato mixture evenly in it. Cover with aluminum foil and bake on the middle rack of the oven for 45 minutes. Remove the aluminum foil and continue baking for 15 minutes. Let cool a little bit before serving.