Place the potatoes into a large pot and cover with salted water. Bring to a boil, then reduce heat to medium-low, cover, and simmer until tender, about 20 minutes.
Drain and allow to steam dry for a minute or two.
While potatoes are boiling, place cabbage into a pot with about an inch of water, bring to a boil, cover, and simmer the cabbage until tender, 10 to 15 minutes.
Drain the cabbage, and set aside.
In a large bowl, mash the potatoes and mayonnaise together, adding chicken broth by the tablespoon until you reach your desired consistency. Season the mashed potatoes with salt and pepper. Stir the cabbage into the mashed potatoes.
Place the cooked ham into a skillet over medium-low heat, and cook and stir until the ham is hot, about 3 minutes. Stir the cooked ham into the colcannon, and serve.
