Dissolve the yeast in the water and milk. Mix it with the rest of the ingredients in a food processor or by hand. Place the dough in a big bowl and cover it with a clean tea towel. Set it aside to rise in a spot with consistent temperature for two hours, until it has doubled or tripled in size.
Knead the dough again (the dough will be a bit sticky, so coat your hands in flour to be able to work with it). Make a hole in the centre of the dough and stretch it to form a circle. Stick the figurine and the bean wrapped in aluminium foil in different spots inside the cake. Once you have formed the typical shape of a kings’ cake, carefully place it on a baking sheet lined with parchment paper, cover it again and let it rise for another hour.
When the dough has doubled in size, heat the oven to 220º C (425º F). Once the oven is pre-heated, decorate the cake with the candied fruits and brush the egg over the top, being careful not to press too hard on the fruits and flatten the cake. Sprinkle sugar over the top, and put the cake in the oven. Immediately lower the temperature to 200º C (400º F) and bake for 10 minutes. After 10 minutes, lower the temperature to 180º C (350º F) and bake for another 10 minutes. Remove the cake from the oven and allow it to cool.