Cut the butter into small pieces and leave it at room temperature for about half an hour.
In a small bowl, beat the eggs, the yolk and the cold water together. If you have a mixer put in the bowl with the leaf.
Dissolve the sourdough starter in the mixture of water and eggs.
In a larger bowl mix the dry ingredients together: the two flours, sugar and salt.
Combine the mixture of eggs, sourdough and water with the dry ingredients and knead, until you have a soft dough (it will not be very soft). If you have a mixer, remove the leaf and insert the hook. It will ball around the hook immediately
Add the pieces of butter one by one and do not add the next until the previous one has been absorbed. If you knead by hand it is essential to do so otherwise you will double the effort.
When the butter has been completely added continue to knead until the dough no longer sticks. If are using a mixer the dough must be completely balled around the hook.
Let the dough rest about a quarter of hour and then make a series of folds.
Put the dough in a glass bowl, cover with plastic wrap and put in the fridge overnight.
Pull out the dough the morning after and wait until it will be at room temperature.
Using a scale divide the dough into 100 gr. loaves, make small balls, gently press them with the palm of your hand and with a two cm diameter stencil make a hole in the center.
Let the little loaf rise until they are quite doubled.
Pour the oil into a deep saucepan and when it has reached 180° fry the donuts one at a time. It is important that the oil never exceeds 190° otherwise externally they will be beautiful in color but raw.
Fry the donuts for 4-5 minutes and let dry on paper towels.
When they are cold, melt the white chocolate and when it is lukewarm, almost cold, (color with edible coloring if you want) glaze the top of the donuts. Repeat with milk chocolate