1. In a large bowl combine flour, yeast, salt and sugar. Whisk until blended.  
2. Combine eggs, milk and butter in a stand mixer fitted with a whisk attachment. Blend until frothy.  
3. Replace the whisk attachment with the hook attachment and add flour mix, one cup at a time, until a slightly sticky dough ball forms.  
4. Spray a large bowl with pan release spray and transfer the dough to the bowl, cover with plastic wrap and set in a warm place in your kitchen. Let the dough rise, doubling in size, for 2 hours.  
5. While the dough is rising, prepare the chestnut cream.  
6. Scald milk in a medium sauce pan over medium low heat (approx. 180°F). In a large bowl, whisk together vanilla, yolks, sugar and flour until blended.  
7. Pour hot milk in a thin stream into the egg mixture, while whisking, to temper. Return the mix to the sauce pan and bring to a simmer, whisking frequently, until thick. Fold in chestnuts, scrape into a sealable container and refrigerate until ready to fill the donuts.   
8. Remove the dough from the bowl on to a clean work surface. Flatten using either a rolling pin or your hands into a 1/2 inch rectangular sheet.  
9. Using a 4 inch round cookie cutter, cut the dough and place on to a parchment lined baking sheet. Cover with plastic wrap, return to the warm spot and let rise for another 2 hours.  
10. In a large dutch oven or deep fryer, heat oil to 350°F.  
11. Carefully add donuts to the hot oil and fry for approx. 2 minutes (working in batches of 2-3 donuts at a time), flipping halfway through until puffy and dark brown.   
12. Remove using a slotted spoon and let drain on a wire rack. Let cool for 10 minutes.  
13. Poke a hole into each donut (being sure not to puncture through the other side), large enough to fit the tip of your pastry bag. Fill a pastry bag with chestnut cream and fill donuts.  
14. Dust each donut in additional sugar before serving.