For the ham and cheese croquetas, melt the butter in a large saucepan, then whisk in the flour and cook for 2-3 minutes. Whisk in the milk gradually to make a thick sauce. Season with salt and pepper.
Stir in the breadcrumbs, ham, cheese 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 croqueta in the flour, then egg and finish with a layer of panko breadcrumbs.
Add the oil to a deep-fat fryer and preheat to 170C/338F. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Deep fry the croquetas in batches until golden-brown. Remove and drain on a plate lined with kitchen paper.
To make the mayonnaise, whisk the egg yolks with the mustard in a bowl and then very gradually add the oil, whisking continuously. Stir through the vinegar, then season with salt and pepper.
Serve the croquetas on a board with a bowl of the mayonnaise for dipping.