In a medium bowl, combine the finely chopped walnuts and sugar.
On a lightly floured surface, roll dough into a rectangle, about 15 inches by 12 inches (38 cm by 30.5 cm).
Brush the surface of the rectangle with melted butter. Spread evenly with a generous layer of the walnuts and sugar.
Roll up the rectangle long side to long side and pinch together the seam to seal. Transfer the roll to the prepared baking sheet seam side down. Push together the ends, pinching the dough together to seal and form a circle.
Make about 1 inch (2.5 cm) thick slices around the circle about 3/4 of the way towards the center. Take care not to cut all the way through to the interior of the circle. Gently turn each slice on its side in the same direction to show off the walnut swirl.
Cover the pastry with a towel and allow to rest for 20 minutes, until slightly puffed.
In a small bowl, beat together the egg and 1 tablespoon (15 milliliters) milk until well combined. Brush over entire surface of the bread.
Bake in preheated oven until golden brown, 20-30 minutes. Allow to cool slightly before transferring off of baking sheet.
This bread is best the day it is made.