In lukewarm milk, whisk the yeast with a little sugar and let it proof for 5-10 minutes until frothy.
In a large bowl, combine the flour, salt, and remaining sugar. Add the yeast mixture, butter, and egg yolks, then knead until you have a smooth dough. Cover and let rise for 1 hour in a warm place.
In a separate bowl, mix the chestnut puree with powdered sugar and vanilla extract until smooth.
Divide the risen dough into two equal portions. Roll each portion into a rectangle.
Spread the chestnut filling evenly over each rectangle of dough. Roll up tightly, like a log.
Place the rolls on a baking sheet lined with parchment paper. Brush the tops with beaten egg and let rest for 20 minutes.
Preheat oven to 350°F (180°C). Bake the rolls for 35-40 minutes, or until golden brown.
Let the Bejgli cool completely before slicing and serving.
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