To make the dough: Heat the milk to 110 degrees F. Add the milk and yeast in the bowl of a heavy duty mixer. Let rest about 10 minutes. Add the flour, sugar, egg, salt, and vanilla and, using the dough hook, mix until well combined. Add the butter in 3 equal additions and mix until well combined. Knead in the mixer on low, about 5 minutes. Divide the dough into 1/4-ounce balls.;
To make the topping: With an electric mixer, cream the lard and confectioners' sugar together in a bowl. Add the flour, baking powder, and vanilla and mix until combined. Roll out the topping on a floured surface into a thin sheet, about 1/8-inch thick. Use a biscuit cutter or knife to cut out circles that are large enough to cover the top of the dough balls.
Preheat the oven to 325 degrees F.
Top each dough ball with a circle of topping and sprinkle them with sugar. Using the back of a pairing knife, scratch the image of a shell on the top of each concha. Arrange on a baking sheet lined with parchment paper. Let rise until doubled in size, about 45 minutes. Bake the conchas about 5 to 7 minutes.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.