1 1/4 cups (risen and deflated) pate fermente, cut into walnut size pieces
3 large egg yolks, beaten
2 1/2 tablespoons honey
3 tablespoons water, plus more if needed
3 tablespoons canola oil, plus more for coating the bowl
For the Topping
3 1/2 cups bread flour
1/2 teaspoon baking powder
1/2 teaspoon kosher salt
1/2 pound plus 6 tablespoons unsalted butter, at room temperature
2 1/2 cups powdered sugar
2 teaspoons pure vanilla extract
3 tablespoons unsweetened cocoa powder
1 tablespoons orange zest
2 tablespoons orange juice
red and yellow food coloring
Start by making the Pate Fermentee the night before you’re going to make the bread dough. It will need to rest in the refrigerator for anytime between 8 and 24 hours.
Put the water and yeast in a large bowl. Add the flour and salt. Use a wooden spoon to stir the mixture into a shaggy dough. Cover the dough with plastic wrap and let stand at room temperature for 30 minutes.
Refrigerate the mixture for a minimum of 8 hours and a maximum of 24 hours. There is no need to return it to room temperature before using it. Deflate it with a wooden spoon or floured fingertips before measuring.
To make the challah bread, place the bread flour, sugar, salt, and yeast in the bowl of a stand mixer fitted with a dough hook. Add the pate fermentee, egg yolks, honey, water, and oil and mix on low speed until the dry ingredients are completely incorporated and the yeast has disappeared into the dough. Add a little extra water if this hasn’t happened in 3 minutes. Increase the speed to medium to medium-high and mix until the dough is smooth, pulls away from the sides of the bowl, has a bit of shine, and makes a slapping noise against the sides of the bowl, about 5 minutes. The dough will look smooth and feel slightly tacky.
Coat the inside of a large bowl with oil and transfer the dough to it. Lightly dust the top of the dough with flour and cover the bowl with plastic wrap. Let stand at room temperature until the dough is puffy and supple, about 1 1/2 hours.
While the dough is rising, make the concha topping.
Whisk together the flour, baking powder, and salt in a bowl.
Place the butter and powdered sugar in the bowl of a stand mixer fitted with the paddle attachment and beat on medium speed until creamy, about 4 minutes. Add the vanilla extract. Add the flour mixture and beat until just combined.
Divide the dough in two. Using the mixer, beat the cocoa powder into one half of the dough. You may need to remove the dough and knead on the counter to evenly combine the cocoa powder. Set aside and wipe out the mixing bowl.
Add the remaining half of concha topping to the mixing bowl. Add the orange zest and orange juice and one drop each of yellow and red food coloring, beat until well incorporated. Again, you may want to move this process to a counter to knead until evenly mixed. Add more food coloring to get your desired orange coloring.
Divide each chocolate and orange toping into three or four pieces and put the topping between two large rectangles of parchment paper alternating the pieces in flavor and color. Press the topping together. Between the two pieces of parchment paper, roll the topping to about 1/2-inch thick. Remove the top parchment, and using a 2 1/2-inch round biscuit cutter, cut rounds. You can save the scraps to reroll.
Use a sharp knife to score each round with a hash mark, being sure to not cut through the entire topping. Let rest at room temperature somewhere cool.
Line two rimmed baking sheets with parchment paper.
Tip the dough onto a lightly floured surface and knead to a smooth ball. Divide into 12 equal pieces (2 1/2-ounces or 70g each).
Form each piece into a roll and transfer the rolls to the prepared baking sheets. Gently top each roll with a scored concha topping round and cover the pan loosely with plastic wrap.
Let the conchas stand at room temperature until they puff slightly and the dough holds indentations when pressed lightly, about 1 hour. As they rise, the topping will bend and start to cover the top of the dough.
Place racks in the middle and upper third of the oven and preheat oven to 350 degrees F.
Bake the puffed conchas until the base is golden brown and the topping is firm to the touch, about 18 to 20 minutes.
Transfer to a wire rack to cool completely. Store in plastic bags for up to 4 days. I like these best the day after they’re baked.