For the dumplings, beat the eggs and milk together in a bowl. Add the chopped ham and pork, breadcrumbs and parmesan, mix until well combined and mould into six small balls.
Place the balls on a plate or tray and chill the dumplings in the fridge for 20 minutes.
Heat the oil and butter in a frying pan and fry the dumplings for eight minutes, turning regularly, until golden-brown all over. Remove from the pan and set aside to drain on kitchen paper. Keep warm.
Fry the black pudding in the same pan for 2-3 minutes on each side, or until crisp, then set aside to drain on kitchen paper. Keep warm.
Meanwhile, for the red wine sauce, heat the oil in a frying pan and fry the onion for 4-5 minutes, or until softened. Add the beetroot, wine, stock and thyme.
Bring the mixture to the boil and cook for 20 minutes, then blend with a hand-held blender to a purée. Pass the sauce through a fine sieve, then return to the pan and heat until the volume of the liquid has reduced by half. Whisk in the butter.
To serve, place a spoonful of sauce onto serving plates, top with a slice of black pudding followed by a dumpling.