Warm the whole milk to 110°F and dissolve the active dry yeast with 1 teaspoon granulated sugar. Let it sit for 5-10 minutes until foamy. If no foam appears, the yeast is dead and fresh yeast must be used.
2.25 tsp active dry yeast, 0.5 cup whole milk, 0.5 cup granulated sugar
In a mixing bowl, combine the all-purpose flour, remaining granulated sugar, salt, eggs, softened unsalted butter, vanilla extract, and the yeast mixture. Knead the dough by hand or with a dough hook for 8-10 minutes until smooth and elastic, ensuring the dough springs back when poked.
4 cups all-purpose flour, 0.5 cup granulated sugar, 0.5 tsp salt, 2 large eggs, 0.33 cup unsalted butter, 1 tsp vanilla extract, 2.25 tsp active dry yeast
Place the kneaded dough in a greased bowl and cover with a damp towel. Let it rise in a warm area at 75-80°F for 1 to 1.5 hours or until doubled in size. Use an oven with a light on if your kitchen is cold.
4 cups all-purpose flour
Punch down the risen dough and divide it into 12 equal portions. Flatten each ball slightly. Mix the powdered sugar, all-purpose flour, softened butter, vanilla extract, and optional cocoa powder until crumbly. Divide topping into 12 portions and press each ¼-inch layer onto each dough ball. Score a shell pattern with a knife or bench scraper. Place the topped balls on a parchment-lined baking sheet.
0.5 cup powdered sugar, 0.33 cup all-purpose flour, 0.33 cup unsalted butter, 1 tsp vanilla extract, 2 tbsp cocoa powder
Cover the shaped conchas loosely and let rise for 30-45 minutes until puffy. Preheat oven to 350°F. Bake the conchas for 18-22 minutes until golden on the bottom and hollow-sounding when tapped. Remove and cool on a wire rack uncovered for 30 minutes.