Add the all purpose flour to the mixer, set with the dough hook, along with the eggs, egg yolk, and salt. Start the mixer over low speed. Meanwhile, add the active dry yeast to 1/2 cup lukewarm water and stir until creamy and well dissolved. Stir it into the flour mixture, and let it continue beating, now over medium speed, for about 3 to 4 minutes.
Incorporate the unsalted butter, keep on beating for 3 to 4 minutes more. Lastly, add the sugar and continue mixing for another 3 to 4 minutes or until the dough is gooey, sticky, elastic and very smooth.
With a spatula, push the dough into a mixing bowl greased with butter or vegetable shortening, cover it with a kitchen towel and place it in the warmest area of your kitchen, where there are no wind currents. Let the dough rise for at least 2 and up to 8 hours. It should have doubled in size.
For the sugar topping, place the flour and confectioners' sugar in a large bowl. Using your hands, incorporate the diced butter into the flour mixture. Mix and knead it until its smooth and homogeneous. If you want half the conchas to be chocolate flavored, separate half of the mixture in another bowl, and mix it very well with the cocoa powder. Cover the sugar toppings with plastic wrap so they won't dry out.
To assemble the conchas, grease thick baking sheets with butter or vegetable shortening and keep your hands greased. They will need to be greased for you to shape the dough. Using your hands, make about 2 inch balls with dough. Then, slightly press them flat, as in a thick disk, but not a tortilla. Leave about 2 inches in between each of the conchas so they will have room to expand.
Once your baking sheet is filled with the dough disks, cover them with the sugar coating. To do this, grab about a tablespoon of sugar coating, plain or chocolate. Make a round ball with your hands and then flatten it thin, like a tortilla. Place it on top of the dough disk and slightly press down. It should cover most of the surface.
If you have a concha mold, press it on the sugar topping. If you don't have one, cut through the sugar topping making round lines or any decoration that reminds you of a shell.
Leave the prepared conchas in a warm area of your kitchen, uncovered, and let them rise again, for about 2 to 4 hours.
Preheat the oven to 350 degrees. Place the conchas in the oven for about 20 to 24 minutes, until the conchas are slightly browned around the edges and look fluffed up.