Slice a lid approx. 2 cm thick off the top of each roll, set aside. Carefully remove the inside of the rolls, leaving a rim of approx. 5 mm. Spread the cream cheese inside the rolls, place 1 slice of ham inside each, lining the roll completely. Mix the cheese and chives, sprinkle half over the top. Crack the eggs into a cup, one at a time. Carefully slide each egg into a roll, season. Scatter the rest of the cheese on top. Transfer the rolls to a tray lined with baking paper, cover with the bread lid.
Bake for approx. 15 mins. in the centre of an oven preheated to 200°C.