In a saucepan, melt butter over medium-high heat, stirring to prevent burning. Add flour and whisk together. Add milk, and whisk until smooth. Add in celery salt and Worcestershire sauce. Take off heat and whisk until combined and smooth. Add in ham, cheese and green onion. Chill at least two hours.
When ready to cook, heat two inches of oil in a large frying pan. Beat two eggs on a plate with a fork until mixed and bubbly. Put about two cups of breadcrumbs on another plate.
Gather a small handful of the ham mixture and shape into a small log, about three inches long by about one inch thick. Roll the log in the breadcrumbs, then dip into the egg, then roll once again in the breadcrumbs.
Place the log in the hot oil, turning once or twice so that all sides are golden. Do this with four or five logs at a time, making sure not to crowd the pan. Drain on paper towel and serve.