Soak the bread briefly in the milk, then mix. Add the mince and all the ingredients up to and including the pepper, knead well by hand until the ingredients have combined to form a compact mass. Divide the mixture into 4 portions and, with wet hands, shape into balls.
Arrange the cheese and the chilli peppers on the ham slices, wrap the ham around to form parcels. Press down onto the raw burgers with your thumbs to make a cavity, put the ham wraps into these cavities, then close the cavities and flatten a little.
Close the lid and grill the burgers for approx. 7 mins. on each side over/on a medium heat (approx. 200 °C.