A great use of leftover ham. Yum!
Make the Thick White Sauce with the first five ingredients. Melt the butter in a saucepan, add the flour, and stir until all of the flour is incorporated. Add the milk and stir over medium heat until the sauce is thickened. Remove from heat.
Chop the ham and onion together in the food processor. Add the chopped meat to the cooled cream sauce and mix well. Season to taste.
Form the ham/sauce mixture into balls, cones, or cylinders. Roll in bread crumbs, then coat with beaten egg, and roll in bread crumbs again. Deep fry in oil (385 degrees F.) until brown. Drain on paper towels.
I chop the ham/onions in batches. You can omit the onion if you prefer, though I think it adds to the flavor.
I do this recipe in stages. I might chop up the ham and onions after a ham dinner and store in the refrigerator. (If you have a lot of the chopped mixture, you can also make a nice deviled ham with the leftover.) Then, I might form into cylinders and do the coating earlier in the day that the croquettes will be served. All that's left is the frying.
I tried baking these instead of frying, but they tend to fall apart. I also tried pan frying with just a little oil. Same thing happened. Still tasty but not pretty. Deep fat frying works best.