Place 5 cups of the flour (625gr) in a large mixing bowl. Stir in the sugar and salt, and set aside.
In a separate bowl, beat together the eggs and egg yolks.
Heat the milk and the butter in a small saucepan over low heat and allow the butter to melt. Remove the saucepan from the heat and allow to cool until the liquid reaches between 100°-110°F (38°-43°C) on a thermometer.
When the milk mixture is ready, prepare the yeast mixture in a separate bowl. Add warm tap water 100°F-110°F (38°C-43°C) to the bowl along with the yeast and stir in 1 tsp. of sugar (4g) Stir once or twice so that the yeast and sugar dissolve. Allow the yeast about 5 minutes to activate and proof.
Once the yeast is activated, slowly add portions of the eggs, the milk mixture, and the yeast mixture to the bowl of combined flour. Stir to incorporate. The dough will be sticky at first. Add more flour, 1 large spoonful at a time, until the dough is too stiff to stir. (NOTE: 10 minutes of kneading time begins when you start to stir the dough together.)
Turn the dough out onto a floured surface and knead with your hands until the dough is smooth and elastic, adding more flour to the surface if the dough becomes sticky. Total kneading time is approximately 10 minutes. Continue to knead until the dough no longer sticks to your hands or to the counter surface. Place the dough in a greased bowl, cover, and allow it to rise in a warm (about 85°F/29°F) draft free environment for 1 hour.
Punch the dough down and allow to rest for 15 minutes. Weigh the dough and divide into 10 equal pieces and form each into a round, domed patty (like a hamburger bun). Place the dough patties on a parchment lined baking sheet. Allow to rise for 1 hour.
While the shaped conchas are rising, prepare the topping. In a small mixing bowl, combine the vegetable shortening, powdered sugar, egg yolks and flour. Press the mixture with the back of a spoon or fork to knead the ingredients together. When the dough is well combined, divide the dough into 4 portions, coloring one portion with the yellow food coloring, another portion with the red food coloring (pink is the desired color) and the remaining portion with the cocoa powder. Leave one portion white. (To divide evenly across 10 conchas, one of the 4 topping portions will have to be smaller for just 2 conchas.)
Heat the oven to 350°F (177°C)
Form the topping dough into equal sized balls. Using a rolling pin or a tortilla press lined with two sheets of plastic, flatten each of the balls into a thin circle that is just smaller than the diameter of the risen bread. Sprinkle extra flour on the rolling surface or in the tortilla press so that the dough does not stick. Place a flattened circle of topping on each of the completely risen breads. Mark each topping using a concha stamp.
Bake the conchas for 25-30 minutes, until they are golden brown around the edges.
