Put the butter into a small saucepan with the milk and 100ml of water. Warm over a low heat until the butter has melted. Set aside to cool for a few minutes.
Put the flour in a large bowl (or the bowl of a freestanding mixer). Add the yeast to one side of the bowl and the salt, sugar and spice to the other.
Beat the eggs into the lukewarm milk mixture, then gradually add this to the dry mixture, stirring all the time, until a sticky dough forms. Knead on a lightly oiled surface (or using the dough hook attachment) for 10-15 minutes or until it is no longer sticky and has become a smooth, elastic dough. Towards the end of the knead, sprinkle over the zest, mixed peel and apricots and fold in. Put the dough in an oiled bowl, cover, and leave in a warm place for 1-2 hours, until doubled in size.
When the dough has risen, turn it out onto the oiled surface and fold it in on itself a couple of times to knock out any large air bubbles. Roll the dough out into a large rectangle approx 40 x 20cm, around twice as long as it is wide. Spread the soft butter all over the dough, then top with the 3 tbsp of marmalade. Tightly roll the dough, starting from one of the shorter sides, then cut into 10 slices and put on a baking tray with enough space for them in a single layer to double in size. Cover the rolls with oiled clingfilm and leave for at least 45 minutes, or until doubled in size (you can also put the buns in the fridge overnight at this stage, to bake fresh for breakfast).
Preheat the oven to 200ºC, gas mark 6. Brush the risen rolls with beaten egg and bake for 15-20 minutes or until golden. Remove from the oven and immediately brush with the 1 tbsp of marmalade. Mix together the icing sugar with enough clementine juice to make a thick icing. Drizzle or pipe over the tops of the buns, then serve warm. These buns will keep for two days, but are best enjoyed on the day they are baked.