Rehydrate the mushrooms in hot water for 7 minutes. Remove stems and slice.
In a large pot, heat up stock and water. Add mushrooms, Teriyaki sauce, garlic, ginger and half the green onion and let boil 15 minutes.
In the meantime heat up a skillet with vegetable oil and slice the canned ham into 1/2 inch slices. Sear each side until golden. To serve place soup in bowl and top with seared ham and the remaining green onion.