Bring a large pot of salted water to a boil and cook potatoes until tender but firm, about 15 minutes. Drain potatoes and transfer to a medium bowl. Mash together with milk.
Place leeks in a medium saucepan with enough water to cover and bring to the boil. Cook 10 minutes or until tender. Drain and set aside.
In a medium frying pan over medium heat, cook and stir the minced beef until evenly brown. Mix in the onion, red pepper and green pepper. Season with green chillies and soy sauce. Continue to cook and stir until vegetables are tender.
In a medium baking dish, mix mashed potatoes, leeks and minced beef mixture. Sprinkle with Cheddar cheese and top with ham.
Bake 25 minutes in the preheated oven, until bubbly and lightly browned.