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• Mix the yeast, milk and sugar in the bowl of a food mixer. Leave for about 15 minutes in a warm place until there is a layer of foam on top. 
• Add the butter, yolks and vanilla extract and mix, with the dough hook, at medium speed. Add half the flour, mix for a minute then slowly add the remaining flour and salt. 
• Mix the dough at medium speed for about 5 minutes then place the dough in a large oiled bowl and cover with a damp cloth or cling film. Leave to rise in a warm place for about 2 hours until doubled in size. 
• Meanwhile prepare the chestnut ganache if using. Mix the chestnut puree with the icing sugar and vanilla extract. Warm the double cream in a pan gently stirring with a whisk. Switch the heat off as soon as it reaches boiling point. Gently pour the hot cream into the chestnut mixture and mix with the whisk so there are no lumps. Leave to cool to room temperature then refrigerate until you need it. 
• After the dough has risen for two hours, tip it onto a floured surface and gently roll out to create a round or oval shape about 1.5-2cm thick. Using a round cookie cutter or a glass, cut out 4-5cm rounds or 7-8cm rounds for larger doughnuts. 
• Place them onto oven trays lined with greaseproof paper, leaving space between them as they will rise more. Cover with cling film and leave to rise for a further 30 minutes in a warm place.
• Heat the oil to 150°C in either a large, deep frying pan or a shallow saucepan. Once hot gently fry a few doughnuts at a time, turning them halfway. They will cook fast, about 20-30 seconds on each side. They should be pale golden. 
• Remove from the oil with a slotted spoon and place in a sieve. After a minute, transfer them to a plate lined with kitchen paper to help absorb excess oil. Repeat with the remaining doughnuts.
• When cooled, fill them with ready-made crème de marron or the home-made ganache or both. Pipe the filling into them with a pastry syringe or a piping bag. 
• Top with marrons glacé pieces, icing sugar or golden caster sugar. 

Makes 20 small or 10 large doughnuts