Combine ham and mustard in a food processor and pulse until it forms a smooth paste.
Melt the butter in a heavy saucepan over medium-low heat. Add the flour and cook, stirring constantly until well blended but not browned, about 2 minutes. In the meantime, gently heat the milk to a gentle simmer but do not let it boil. Gradually stir in the milk, whisking constantly until the sauce has thickened and is pulling away from the sides of the pan. Remove from heat. Add the pureed ham and mix until well combined. Season with salt, pepper and nutmeg.
Pour the mixture onto the lined baking sheet using a rubber spatula to spread evenly. Bring to room temperature then cover with plastic wrap and refrigerate until set, at least one hour.
Lay out 1/2 cup of flour, beaten eggs, and bread crumbs in separate mixing bowls. Dust hands with flour and spoon the béchamel mixture into walnut sized pieces and roll into desired shape, about one tablespoon per croqueta. One by one, roll the croquetas in flour, drop into the egg mixture with a fork or slotted spoon, then transfer to bread crumbs. They should be completely coated in bread crumbs so they don’t leak when cooked.
Add about 3″ of oil to a large heavy skillet. Heat over medium-high heat to 375°F (see header). Working in batches, carefully add the croquetas. Gently turn until brown on all sides, about 2 minutes. Remove with a slotted spoon and drain on paper towels or re-purposed grocery paper bags. Serve immediately.