Have each ingredient ready and measured (by weight) before starting, and thoroughly read the notes above.
Mix the all-purpose flour, yeast, sugar, and salt in the bowl of a stand mixer at medium speed, just to mix it well.
Add the butter and mix well (using the stand mixer with the hook attachment), then mix in the eggs and vanilla extract and slowly pour the milk in little by little until the dough looks cohesive.
Keep beating the mixture for about 7 minutes at medium speed.
Add a little more flour around the inside of the bowl (2-3 tablespoons), just enough for the dough to separate from the container.
The dough should be soft and slightly sticky.
Place the dough on your floured working table and knead it just enough to shape it into a ball.
Place this ball in a large greased bowl to rest. Cover it with plastic wrap (or wax paper) and a kitchen napkin.
Let the dough rest in a warm place for about 2 hours until it doubles in size.
While the dough is rising, prepare the sugar topping by softening the shortening and mixing it with the confectioner’s sugar and flour.
Once the dough has risen and doubled in size, place it onto a floured surface and let it rest for about 5 minutes.
Divide the dough into 16 small balls (60 grams each).
Shape the balls and place them onto greased baking sheets.
Grease the top of each ball with a little shortening.
Divide the topping paste into 16 balls and press down on each one to form a small, flat circle.
Place this disk onto the ball of dough, and press it down very firmly.
Use a concha cutter or a knife to decorate them with the traditional concha shape.
Allow the conchas to rise in a warm place until they are almost double in size.
Bake in a preheated oven at 325º degrees for 20 minutes, or until the bottom of the conchas are lightly golden.
