Prepare the dough. In a small bowl, whisk together 1 tablespoon of the granulated sugar, the active dry yeast, and the warm milk. Cover with plastic wrap and let the yeast bloom until it’s very foamy for 10 minutes.
In the bowl of a stand mixer (or a large separate bowl), whisk together the flour, the remaining granulated sugar, the brown sugar, pumpkin pie spice, salt, cinnamon, and nutmeg.
Using a paddle attachment, mix in the softened butter until coarse and crumbly.
In a medium bowl, whisk together 2 eggs and the pumpkin puree until well combined. Set aside.
Using a dough hook attachment, slowly add the yeast mixture to the dry ingredients, followed by the egg and pumpkin mixture. Mix on medium speed for 5-6 minutes (or mix by hand), until the dough becomes smooth and elastic. The dough will be tacky and sticky.
Transfer the dough to a large greased bowl and cover with plastic wrap. Allow the dough to rise in a warm place until doubled in size, about 1 ½ to 2 hours.
Prepare 3 baking sheets with parchment paper and set aside.
Uncover and punch the dough down, then allow it to rest for 5 minutes. Section the dough into 12 pieces and roll into balls. The dough will still be sticky, so you can grease your hands with oil or cooking spray to make it easier to handle, but do not add more flour.
Place 4 dough balls onto each baking sheet, cover with plastic wrap or a kitchen towel, and allow it to rise again for 45 minutes to 1 hour until the dough has doubled in size.
While the dough rises, make the concha topping. Beat together the flour, powdered sugar, butter, vanilla extract, and gel food coloring in a stand mixer with a paddle attachment until fully combined. The topping should be soft and moist, like the consistency of Play-Doh. If not using immediately, form the topping into a ball and cover with plastic wrap until ready to use.
Divide the topping into 12 balls, then lightly flatten each ball in between two sheets of plastic wrap using a tortilla press. You could also use a rolling pin to shape the topping into rounds.
Assemble the conchas. Preheat the oven to 350°F. In a small bowl, beat the remaining egg and brush each risen concha with egg wash.
Carefully remove the rolled-out topping from the plastic wrap and drape it onto the risen concha dough. Lightly pat it down to secure the topping onto the dough.
Cut grooves into the topping using a paring knife so it resembles a clamshell, a crisscross pattern, or whichever pattern you prefer.
Bake for 15-17 minutes until the dough is lightly golden brown. Transfer to a cooling rack and allow to cool for 10 minutes before serving.
Notes
Make sure your yeast is alive before adding it to the dough. If the milk and yeast mixture is bubbly and frothy, that means the yeast is alive and thriving. If it’s not, that means the yeast is likely dead, and you need to start over with a new yeast packet.
To make shaping the topping a little easier, you could use a concha shell cutter.
The dough will be sticky and tacky. To make it easier to hand and shape the concha dough, you can lightly grease your hands with oil or cooking spray, but I do not recommend adding more flour.
Don’t overcrowd your baking sheet. The conchas expand even more in the oven, so make sure you don’t overcrowd your baking sheet or the conchas will not have proper ventilation and will release too much heat, resulting in burning the bottoms before they’re fully baked.
Storage: Store leftover conchas in an airtight container in a cool and dry place for up to 5 days.