Bring a large pot of water to a boil; add potatoes and carrot. Return mixture to a boil and add eggs; cook until potatoes are tender, 20 to 30 minutes. Drain and slightly cool mixture. Chop potatoes and carrot; peel and chop eggs.

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Mix potatoes, carrot, eggs, pickles, peas, ham, and parsley together in a large bowl; stir in mayonnaise until salad is evenly coated.