For the panettone, grease a 12-hole, deep-sided muffin tin with butter.
In a bowl, mix the candied peel, sultanas and cranberries with the spiced rum until combined. Set aside.
Add the flour, sugar and salt to the bowl of a food mixer. Whisk the yeast with a little of the water in a separate bowl until dissolved. Add the yeast mixture to the flour, then add the remaining water and the whole eggs and beat until the mixture comes together as a dough. (This can also be done by hand or using a hand-held electric whisk.)
Beat in the butter a little at a time, then add the orange zest and continue to beat for 4-5 minutes, or until the dough is smooth.
Set the dough aside, covered, in its bowl, to prove for about 1 hour, or until it has doubled in size.
Knock back the dough, sprinkle over the dried fruit, then knead the fruit into the dough, either in the bowl, or on a lightly floured work surface (it will feel very sticky).
Roll the dough into a ball and cut it into 10-12 equal-sized pieces. Roll each piece into a ball on a lightly floured work surface. Place one into each hole of the muffin tin. Cover the tin with cling film then set aside to prove again for about 45 minutes, until risen.
Preheat the oven to 190C/170C Fan/Gas 5.
Brush the top of the risen panettone dough with the egg wash, then bake in the oven for 18-20 minutes, or until golden-brown and risen. Remove from the tin and set aside to cool on a wire rack.
For the rum butter, beat the double cream in the bowl of a free-standing food mixer for 3-5 minutes, or until it turns to solid fatty lumps with a liquid base. Cover the mixer with a clean tea towel or muslin cloth halfway through beating, because the liquid will spatter everywhere as it starts to separate!
Line a large bowl with the same tea towel or muslin, then tip in the mixture. Bring the cloth together at the edges to encase the solid butter and squeeze out all the liquid. Discard the liquid.
Tip the butter back into the bowl and beat in the soft light brown sugar for 3-4 minutes, or until pale and fluffy, adding the rum a little at a time.
Spoon the rum butter into sterilised jars and seal. Chill in the fridge or freeze until needed, or serve immediately alongside the warm panettones.