Finely grate your carrot either by hand and place in a mixing bowl or jug. It needs to be finely grated so it cooks through (otherwise they will be crunchy). (In the Thermomix, grate 3 seconds speed 4 or until finely grated).
Add the flour, spices, bicarb, baking powder, salt and sugar. Mix to combine (Thermomix reverse, 5 seconds, speed 3).
Now add the egg, vanilla, yoghurt and milk and mix to just combine (Thermomix reverse, 5 seconds, speed 3).
Heat the butter, ghee or coconut oil in a moderately hot pan, but turn it down to a low to medium heat flipping once the mixture bubbles. Try not to cook to fast (on a high heat) as you want to give the carrot a little time to cook.
To make the spiced cream cheese simply mix all the ingredients together.