Dough:

1. Combine flour, sugar, cocoa, and salt in the bowl of food processor and pulse. Add butter and lard and pulse a few times more until crumbly. Add water and process until the dough comes together, adding a tiny bit more water if necessary until it pulls away from the sides of bowl..
2. Filling:
3. Stir butter and milk together in the bowl of stand mixer or a medium mixing bowl until smooth. Add salt, vanilla, and cornstarch and stir to combine. Mix in powdered sugar a cup at a time until combined then beat until fluffy. Add cookie pieced and beat just long enough to mix them into filling.

Assemble:

1. Roll pastry dough out on a lightly floured surface into a rectangle roughly 1/8 inch thick. Cut into smaller rectangles, about 2 1/2 x 5 inch pieces.
2. Spoon about 1 heaping tablespoon of filling onto the centers of half of the rectangles you've cut and spread to within 1/2 inch from edges, then rub edges with water. Place the other half of the pieces on top of fillings and use a fork or your fingers to crimp the ends together to seal well. Place on a parchment lined baking tray about 1/4 inch apart and place tray in refrigerator for about 30 minutes.
3. Meanwhile, preheat oven to 350 degrees F (180 C). When oven is ready, remove trays from fridge and bake for 10 - 12 minutes until the edges are starting to darken and crisp. Remove tray from oven and cool tarts completely before adding icing.