Dice cooked potatoes. Heat olive oil in a frying pan over high heat. Add the potatoes, stir, lower heat to medium. Let brown 2 minutes, stir, cook another few minutes. (Repeat if you want - the goal is browned crisp cubes of potato.) Reserve to plate, keep warm.
Put cubed leftover ham in hot pan. Again, brown, stir, brown... Ham may release liquid. If so, let most of it cook off and the ham start to caramelize.
Add cabbage. Stir with the ham. Add 1/4 water, stir to deglaze the pan and bring the caramelized bits up and mix them in with the cabbage. Cook until cabbage is done to taste - 3-5 minutes.
Serve hand and cabbage mixture over potatoes.