Prepare Dough

Place the water and yeast in the bowl of a stand mixer fitted with a dough hook and beat to incorporate. Allow the mixture to rest a few minutes as you continue.

Mix the milk, butter, and egg together in one bowl and the remaining dry dough ingredients in another. With the mixer on low speed, add the liquid ingredients to the yeast mixture and beat 15 seconds, until incorporated. Add half the dry ingredients and beat slowly until blended, about 1 minute. Add the remaining dry ingredients and beat again until blended. With the mixer on medium-high, beat 3–4 minutes, or until the dough starts pulling away from the sides of the bowl. Stop and pull some of the dough between your fingers: it should be very elastic and only slightly sticky.

First Rising

Transfer the dough to a lightly floured surface and knead until smooth, 3–4 minutes. Place it in a large buttered bowl and turn to coat with the butter. Cover with a towel and allow to rise in a warm place 1 hour, or until doubled in volume.

Prepare Flavored Toppings

Cream the sugar and butter in the bowl of the mixer until lightened and fluffy. Beat 1 cup (125 g) of the flour into the mixture until a stiff paste forms. Divide this paste into thirds and place each third in a small mixing bowl.

Mix the vanilla and the remaining 1 tablespoon (8 g) of flour into one-third of the paste; mix the canela into another; and mix the cocoa into the final third. Divide each of these flavored toppings into 4 equal balls of about 1 ounce (32 g) each. Pat them into round, flat shapes and set aside. You will have 12 of the flavored toppings.

Form Conchas and Second Rising

Butter a baking sheet and set aside. When the yeast dough has doubled, punch it down and transfer to a lightly floured surface. Pat the dough into a large pie shape and, with a long knife, cut it into 12 equal wedges as you would a pie. Shape the wedges into balls, turning the floured, dry side in and the damper side out.

Place the dough balls on the baking sheet about 3 inches (8 cm) apart. Pat them into round and slightly flatter shapes. Place the circles of flavored toppings on top of the dough balls and pat down lightly to seal; the toppings will cover the entire top of the dough ball and extend down the sides about halfway. Cover with a towel and allow to rise in a warm place until doubled in volume, about 45 minutes.

Preheat the oven to 375 degrees F (190 degrees C). When the Conchas have risen and just before baking, use a sharp knife or a razor blade to cut radiating grooves like a scallop shell into the topping. Bake until pale golden brown, 30–45 minutes, depending on your climate and oven conditions.