While the dough is rising, you can prepare the sugar topping. Soften the shortening with your spatula until it is very creamy, and then add the confectioner’s sugar. Finally, add in the flour little by little (if using, add the ground cinnamon in this step). Set this paste aside to use later. If you’re making half of the Conchas with the chocolate topping, then divide the paste in two and add the cocoa powder to one half, mixing it until it integrates very well.
Once the dough has risen and doubled in size, place it onto a floured surface and let it rest for about 5 minutes. Divide the dough into 16 small balls (60 grams each). To shape the balls, lightly flour your hands and place each small ball on the working surface and gently press down with your hand, rotating your hand to form the balls.
Place them onto greased baking sheets and continue until you’ve finished shaping all of the dough.
Using your hands, grease the top of each ball with a little shortening. Do not skip this step, as it will help the topping adhere to the dough.
To add the topping, flour your hands and divide the topping paste into 16 balls. Use your hands to press down on each one to form a small, flat circle (I like to use a sheet of plastic, like when making tortillas). Place this disk onto the ball of dough, and press it down very firmly.
Once you’ve finished placing the topping on the buns, use a concha cutter or a knife to decorate them with the traditional concha shape.
Allow the conchas to rise in a warm place until they are almost double in size. Depending on the temperature of your kitchen, this step could take anywhere from 1 to 2 hours. Do not leave them to rise any longer, because if you let them grow too much they will collapse inside the oven. Bake in a preheated oven at 325º degrees for 20 minutes, or until the bottom of the conchas are lightly golden. If you are placing more than one baking sheet in your oven, rotate them after 10-12 minutes. Move the sheet on the bottom rack to the top rack and vice versa to have an even baking.
I hope you try this recipe and enjoy the results. Baking (with or without yeast) can sometimes be tricky, and it can help to try out different recipes to see what works for you. There are many other concha recipes out there on the web, for example, the one at Pati’s Mexican TablePati’s Mexican Table or the one from Marcela Valladolid. The only recipe I’m not very confident about is the one at the King Arthur website, since it is very different than a regular concha recipe you will find in Mexico.