Cut the ham into small 1/4-inch cubes. Heat 1 tablespoon of the vegetable oil in a non-stick skillet over medium-high heat. Fry the ham cubes until they are browned on all sides, about 4 to 5 minutes. Drain them on paper towels.
In a medium sized pot over medium heat, add the milk, butter, and processed cheese. Cook just until the cheese melts; don’t let it boil. Add the macaroni, Cheddar cheese, and browned ham and mix well. Pour this mixture into a bowl and refrigerate it for at least 1 hour to firm up.
Heat a deep fat fryer to 375 degrees F. (Alternately, heat 2 inches of oil in a deep cast iron skillet.)
Scoop out the firm macaroni and cheese and form small 2-inch balls. Roll them in the breadcrumbs. Working in batches to avoid crowding the pot, fry the balls for about 2 minutes, or until they are golden brown. Drain on paper towels and serve immediately.