Place the ham, mashed potato, parsley, chilli and gherkins into a bowl and mix to combine well. Season well with salt and freshly ground black pepper.
With floured hands, mould small amounts of the mixture into 7.5cm/3in long cylinders.
Dredge the croquettes in the flour, then dip into the beaten egg and finally dip into the polenta to coat completely.
Heat the oil in a frying pan over a medium heat. Add the croquettes and fry, turning occasionally, until crisp and golden-brown all over. Remove from the pan and drain on kitchen paper.
For the sauce, melt the butter in a pan over a medium heat, then add the flour. Cook, stirring well, for 2-3 minutes.
Add the milk, a little at a time, stirring constantly. Keep adding the milk and cooking until you have a smooth sauce.
Add the parsley and lemon juice, then season, to taste, with salt and freshly ground black pepper.
To serve, place a few croquettes onto each plate and drizzle with the sauce.