In a small saucepan, scald the milk by heating it to boiling then remove from the heat, add the butter and leave it to cool slightly. Skim if necessary.
Add the flour, sugar, yeast, salt and spices to a large bowl.
When the milk has cooled to ‘blood temperature’ (37C/98.6 F), make a well in the centre of the flour mixture, then pour in the warm milk mixture and add the egg.
Mix well with a wooden spoon, then use your hands to bring everything together into a sticky dough.
On a lightly floured work surface (or in a stand mixer with a dough hook), knead the dough until it’s smooth, about 10 minutes by hand or 5-7 minutes by machine.
Lightly oil a bowl with the sunflower oil and add the dough, then turn it to coat with the oil. Cover the bowl with oiled clingfilm and leave to rise in a warm place until doubled in size (1-1 ½ hours).
Heat the oven to 200C/400F and line 2 baking trays with baking parchment.
Peel and grate the carrot, then wring it out in a clean tea towel to remove excess moisture. Add it to the bowl of dough along with the raisins and crystallised ginger. Knead the dough in the bowl to evenly distribute.
Divide the dough into 12 equal-sized pieces and shape into small round buns. Place them onto baking trays (leave space for them to expand) and cover with oiled clingfilm. Leave to rise again until doubled in size (approx 1 hour).
In a small bowl, mix the flour for the crosses with 4 tablespoon of water to make a thick paste (the consistency of toothpaste), adding further tablespoons of water sparingly if needed.
Spoon the flour paste into a piping bag with a small nozzle and pipe a line along each row of buns, then repeat in the other direction to create crosses.
Bake for 20 mins or until golden brown then allow to cool on a wire rack.
Heat the apricot jam, then use a pastry brush to brush it onto the tops of the warm buns and allow to cool.