Special equipment: Pastry scraper: To aid in kneading the dough Wire strainer or other sifting device Shallow baking sheets: The largest that your rack will accommodate. The sides should be no higher than 1-inch to allow for even heat exposur
To set up: Brush a 5quart bowl with melted butter and set aside to rise dough.
To assemble dough: Heat the milk with the butter and pour it into a large mixing bowl. Add 1/2 cup warm water and the shortening. Add the sugar, salt, egg and yolk. Mix well. Dissolve the yeast in 1/4 cup warm water with a pinch of sugar. When the yeast is dissolved, add it to the mixing bowl, along with enough of the sifted flour to create a dough that is not easily stirred. Turn dough out on to a floured work surface and knead until smooth and elastic, adding only as much flour as needed to keep dough from sticking to your hands and work surface. When correct texture has been reached, place dough into the greased bowl. Cover the bowl with greased plastic wrap and let the dough rise in a warm, draftfree spot for 2 hours.
Note: You will not need all of the flour. Save the remaining flour as your dusting flour when shaping your buns.
To rise dough twice: After 2 hours has elapsed, uncover dough and punch it down several times. Turn over in the bowl. Recover bowl and let rise 1 hour more.
To set up to bake: Line 2 shallow baking sheets with parchment paper and sprinkle paper with cornmeal.
To shape buns: After the second rise has been completed, uncover dough and punch down once more. Turn dough out on to a lightly floured surface. Knead briefly and gently. Divide dough into 10 equal pieces and cover all while you work with one. Shape each piece of dough into a smooth ball by first making it round with your hands. Then pull the dough up, pinching at the top of the dough ball. Keep pulling and pinching up at the top until you have a tight ball. Turn ball on its side on the lightly floured surface. With a pastry cutter, cut ball of dough directly in half through the waist of the ball (not through the pinched end). Take one half and place it on top of the other, meeting the cut sides in the middle. Pinch around the circumference of the circle of dough to seal. Flatten the circle gently, but firmly. Shove the pinched seam gently under the bun as you flatten. Lay the buns on the two prepared baking sheets and cover with kitchen towels. Let rise for 30 minutes. Begin timing the rising period after the last bun has been formed.
If topping buns: If you will be topping the buns before baking, immediately after shaping, brush tops of unrisen buns with 1 egg white mixed with 1 teaspoon water. Sprinkle with sesame or poppy seeds or top with either of the onion toppings listed with the ingredients.
To bake: Preheat the oven to 375 degrees F for the last fifteen minutes of the rise. Meanwhile melt some butter in a small saucepan. After the rise, uncover buns and brush the tops with melted butter (brush over topping, if using).
Bake buns in the center of a preheated 375 F oven until golden, about 25 to 30 minutes. Remove from the oven and brush once more with melted butter. Remove the buns to wire racks to cool thoroughly before slicing and enjoying.
To store: Store cooled buns in a large heavy duty plastic bag. If you want to freeze them, double the bag before placing in the freezer. To thaw, let sit on the counter in its original bags until soft.
If you have only one oven and your baking sheet can not hold all ten buns, bake together using the upper and lower third of the oven and switch positions half way through the baking process. Squeeze out as much air as possible from the plastic bags before storing.