Start by grating the carrot finely.
In a bowl, mix the flours, sugars, cinnamon and nutmeg.
Then add the oil and eggs and stir until smooth. Finally, add the carrot and yeast and stir to incorporate.
Put the dough in a greased shape with oil and wheat flour and take it to the preheated oven (200°) for 45 minutes (do the toothpick test). Remove from oven and let cool for 30 minutes before unmolding.
For the frosting, beat the cream cheese, sugar and cream in a mixer for approximately 2 minutes.