To make the dough, warm the milk in a glass measuring cup to about 110°F. Stir in 1 tablespoon of the granulated sugar along with the yeast. Allow to rest until bloomed, about 10 minutes. If the yeast doesn't activate, throw it out and start over.
In the bowl of a stand mixer, fitted with the dough hook attachment, whisk together the flour, remaining sugar and salt. Add the melted butter, eggs, and the yeast mixture. Mix on low until the dough starts to come together. Raise the speed to medium and knead until the dough pulls away from the sides of the bowl and becomes smooth and soft, about 8 to 10 minutes. If the dough is very sticky, add a tablespoon of flour at a time until it pulls away from the bowl.
Once kneaded, add the crushed chocolate cookies and mix until just combined, you want streaks throughout the dough but not fully combined. Transfer the dough to a large greased bowl. Cover loosely with plastic wrap and a damp kitchen towel. Allow to rest in a warm spot until doubled in sized, for 1 hour and half.
Meanwhile, to make the topping, in a large bowl, beat the vegetable shortening until light and fluffy. Add the powdered sugar and flour and mix until it comes together and is pliable and somewhat soft. Add the crushed chocolate cookies and mix until just combined. Wrap in plastic and allow to rest at room temperature until ready to use.
Once the dough has risen, punch it down to deflate and then transfer to a lightly floured work surface. Cut the dough into 12 even pieces (roughly 85g each). Use your palm to roll the dough pieces into smooth balls. Place onto two baking sheets that have been lined with parchment paper, with enough space for spreading. I do six per baking sheet. Cover the pans with plastic wrap and allow to double in size once again, for 1 hour.
30 minutes before the resting time is done, preheat the oven to 350°F.
Divide the topping into 12 even pieces and roll each into a ball. Flatten out into a thin round about 1/4-inch thick, either by hand or with a tortilla press. Place this over the risen dough and use a sharp paring knife to score the top slightly. You can also use a concha cutter. Bake until lightly golden brown around the edges, about 20 to 22 minutes. Remove from the oven and allow to cool slightly before serving. Leftovers can be stored in an airtight container for up to 2 days. Enjoy!