Cover potatoes with water in a large pot and bring to a boil. Cook until tender, about 10 minutes. Drain and add butter and milk while mashing. Set aside.
Heat oil in pan; add onions and garlic and turkey, cook until well browned. Set aside. Drain liquid and add all other ingredients. Mix gently.
Spread turkey mixture on the bottom of a baking dish. Spread a layer of mashed potatoes on top.