Mix everything together and pat turkey into small, flat, burger-sized balls. Chill in the fridge about 1 hours.
Heat the pan with oil and place turkey balls in pan when hot. Cook each side until brown; add 1 small pat of butter to each side. Cook until medium pink and juicy; melt 1 slice of cheese over each burger.
Heat 2 burger buns on both sides in the oven at 350°F.
Dress the burgers with cranberry relish, Walla Walla sweet onion, and iceberg lettuce.