Cook the potatoes and carrots in water or steam them until tender but not overcooked. Drain and let cool slightly. Boil the eggs.
Peel the potatoes, carrots, and onion. Peel the boiled eggs.
Dice all the vegetables and eggs into small cubes. Drain the peas.
Gently mix the potatoes, carrots, onion, pickles, eggs, and peas. Add the mayonnaise, season with salt and pepper, and combine carefully to avoid crushing the vegetables.
Place a generous spoonful of the vegetable mixture onto each ham slice. Roll up the slices and secure them with a chive sprig.Refrigerate until chilled. Serve on a platter or individually on plates.