Always a good idea to read the Helpful Hints, above.
Melt the vegetable shortening in a small saucepan, or even in the microwave. Set aside to cool slightly.
In the bowl of an electric mixer fitted with the whisk attachment, beat all 15 egg whites for approximately 5 minutes over medium speed. Continue to beat until they are very fluffy.
To the egg whites, with the mixer still working, add the 12 egg yolks, a few at a time. Continue to beat for approximately 3 – 5 more minutes. Periodically, using a rubber spatula, push down any of the egg which has found its way onto the side of the mixing bowl.
When well incorporated, pour the beaten eggs into a very large bowl. Wash out the bowl of the mixer and add the melted vegetable shortening. Beat over medium speed for about 3 minutes. Slowly add in the granulated sugar. Continue to beat well over medium speed.
Meanwhile, in a small saucepan mix together the milk and the ammonium carbonate. On medium heat, stir continuously with a whisk, until the milk looks like it is going to bubble over (approximately 5 minutes). At this point, pour the milk + ammonium mixture carefully into the mixing bowl which contains the vegetable shortening and sugar. Turn off the mixer while you are making this addition. Stand back…it’s going to smell! Turn mixture back on and whisk together for another 2 – 3 minutes. To this mixing bowl, add 1 cup of all purpose flour. Mix well until all ingredients are well combined.
In a small bowl combine the baking powder, the vanilla powder and 1 cup all purpose flour. Mix well.
Now, into the large bowl where you have your eggs you will add the various combinations of ingredients. Add the flour/baking powder/vanilla powder combination. Add the vegetable shortening/sugar/milk combination. Then, add an additional 11 cups of all purpose flour.
With your hands, mix all ingredients well. You are almost massaging the ingredients together to incorporate everything. After mixing everything together add an additional 1 cup of all purpose flour. You should get to the point where you can knead the dough in the bowl.
You may need to add 1/4 – 1/2 cup more flour if your dough is still wet. Keep in mind that the dough for the koulourakia will be sticky. Cover the dough with a clean kitchen towel and set aside for 15 – 20 minutes. This period of rest will allow the dough to “stiffen” up a bit, making it easier to work with. If you’re not sure if you need to add more flour, bake a few as a sample, if they flatten out too much, then you need to add a little more flour, perhaps 1/4 cup-1/2 cup.
Line your baking sheets with parchment paper. Preheat your oven to 400 degrees Fahrenheit.
Start forming your koulourakia. Take a small piece of dough (about the size of a walnut) and roll it into a long strip. Fold this strip in half and then twist the two halves together. This makes the traditional twisted shape. Alternatively, you can make a circle with your long strip. You can also make any kind of shape you like, so long as they are all pretty much the same size. You can watch a video here.
Prepare your egg wash by mixing together the 3 egg yolks, milk and water. Brush on top of each koulouraki.
Bake in top third of the oven for 20 – 25 minutes (or mid rack, for 14-18 minutes) until a beautiful golden colour. Let rest a couple of minutes on the baking pan, then transfer them to a wire rack to cool.