In a large mixing bowl combine the yeast, water and sugar and mix well and allow to sit for about 10 minutes for the yeast to get activated.
Add the egg, milk, yogurt and melted butter and mix well with a whisk.
Add one cup of flour, salt, baking powder and powdered sugar and mix well with a spatula. Gradually add the remainder of flour, and switch to using your hand to bring the dough together.
Gently knead the dough on a lightly floured surface for about 5 minutes until you have a soft but not too sticky dough. Add a little more flour if needed.
Place the dough in a lightly greased wide bowl and turn over to make sure all sides of the dough are lightly covered with oil. Cover the bowl with plastic wrap and allow to rise at room temperature for 2 hours. The dough should have doubled in size by this time.
While the dough rises, prepare the filling by placing all the ingredients in a food processor and pulsing until you have a creamy walnut paste. Remove from the food processor and divide into 10 equal pieces.
Once the dough has sufficiently risen, turn it out on a lightly floured surface and roll the dough into a log about 10 inches long. Cut the dough log into 10 pieces.
Preheat the oven to 350℉, adjust the oven rack to the middle position and line a baking sheet with parchment paper.
Prepare the glaze by combining the egg yolk, milk and saffron. Whisk to dissolve the saffron into the mixture. Set aside.
Shape each piece of dough into a ball and press it out to a flat round disc, about the size of your palm.
Place the filling in the center of the disc and bring the edges together by pinching and twisting the edges to secure the filling. Place the pinched side on the counter and gently flatten the stuffed dough by pressing the palm of your hand on top of the pastry.
Place 5 pastry buns on the baking sheet, leaving 1-2 inches of space to allow for pastry to rise and expand.
Using a round cookie cutter, make decorative indentations on the surface of the pastry, pushing down gently to break through the top surface.
Thoroughly brush the surface of each pastry with the egg wash.
Place in the oven and bake for 15 minutes or until the pastry has slightly risen and turned golden.
Remove from the baking sheet and set aside to cool. Bake the remainder of the pastry buns.
Once completely cooled, store in an airtight container in the refrigerator.
Serve Koloucheh with a hot cup of Persian tea or with a cold glass of milk.