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 a boil. Cook 10 minutes, or until tender. Drain, and set aside.
In a medium skillet over medium heat, cook and stir the ground beef until evenly brown. Mix in the onion, red bell pepper, and green bell pepper. Season with green chile peppers and soy sauce. Continue to cook and stir until vegetables are tender.
In a medium baking dish, mix mashed potatoes, leeks, and ground beef mixture. Sprinkle with Cheddar cheese, and top with ham.
Bake 25 minutes in the preheated oven, until bubbly and lightly browned.