Melt the butter in a large saucepan, then whisk in the flour and cook for 2-3 minutes. Whisk in the milk slowly until you have a very thick sauce. Season with salt and pepper.
Stir in the breadcrumbs, both hams and parsley. Place in the fridge to chill for 3-4 hours.
Shape the chilled mixture into 7cm/2¾in cylinders. Place the flour, beaten eggs and breadcrumbs in three separate bowls. Coat each one in the flour, then egg and finish with a layer of breadcrumbs.
Add the oil into a deep-fat fryer and preheat to 170C/338F. (Caution: Do not leave hot oil unattended.)
Deep fry the croquetas in batches until golden-brown. Remove and drain on kitchen paper.
To make the mayonnaise, whisk the egg yolks with the mustard in a bowl and then very slowly and gradually add the oil, whisking continuously. Stir through the vinegar and garlic, then season with salt and pepper.
Serve the croquetas on a board with a bowl of mayonnaise for dipping.