In a small bowl, mix the cornstarch in ¾ cup of the milk and set aside.
Prepare a baking sheet tray with at least a one inch edge. A cookie sheet works well.
In a saucepan, warm the milk and set aside or keep on low heat until needed.
Heat a medium sized pot over med-low heat, add the butter and olive oil and sauté the onions until soft and translucent. Add jamón and lightly sauté 1-2 minutes.
Add the flour to the pot and mix to form a roux. Pour the milk slowly and mix with a whisk. Add the nutmeg and add the cornstarch mixture. Mix well and cook over low heat for 5 minutes. Add cheese and mix until melted another minute or so. Then pour onto the baking sheet tray and spread it out evenly. Let cool for one hour, uncovered.
Fill a pastry bag with the cooled mixture and cut off the tip of the bag to make a 1 inch hole. Prepare your second sheet tray with about 1/2 inch layer of flour. Pipe a long tube of mixture onto the tray and continue until you have piped all of the mixture onto the tray and you have about 5-6 tubes.
Cut into 2-3 inch logs and dredge well in flour on all sides. In a shallow dish, beat the eggs with a little water and spread breadcrumbs onto a sheet tray or shallow dish. Dredge each croquette in the egg mixture, then the breadcrumbs and place on a clean tray.
Fill a heavy pot with enough frying oil to be 2-3 inches deep. Heat to 350 F and fry in batches until golden brown on each side. Serve warm with sauce.