In a bowl, combine the yeast, honey and water. Let set for 10 minutes.
In the stand mixer, cream together the 1/2 cup sugar and 1/4 cup shortening. Mix in the eggs, salt and yeast/water mixture. Gradually mix in the 4 cups of flour, turning up the speed, as needed. You may have to stop and scrape the sides down with a spatula from time to time.
The dough should pull away from the sides of the stand mixer when ready. If it's still too sticky, mix in a little more flour. I sometimes find it easier to transfer the dough to a flat work surface to finish kneading.
When ready, transfer the dough to a greased bowl. Cover and let rise for 1 to 1 1/2 hour. It must rise in a warm place. I heat my oven to 200 degrees and keep the covered bowl near the warmth of the oven.
Once it proofs, punch down and divide into 12 balls. If the dough feel sticky, dust it with a little flour to help shape the conchas. Place on greased baking sheet, press down lightly. Cover loosely with a lightweight kitchen towel and let rise for 1 more hour.
While the conchas rise the last hour, prepare the topping. Mix the flour and sugar first. Then work in the vanilla and shortening. If it's too dry, add a little bit more shortening. If it's too sticky work in a little more flour and sugar(equal parts).
When ready, roll 2 tablespoons of topping into a ball and flatten into a round disc. You can use a tortilla press to do this step. Place over conchas and score with a knife, careful not to cut into bread. See notes below for variation on the topping.
Bake in preheated 350 degree oven for 20 minutes, rotating pan halfway through baking time. The bottoms of bread should be golden brown. and lightly golden on top. Let cool completely before storing in an airtight container with a slice of sandwich bread. This will help them stay moist for a couple of days. Best thing to do is to enjoy them while they are fresh.
PLEASE read my updated notes on the concha recipe before starting.