Remove dough from refrigerator and place on a flour-dusted surface. Pull the edges of the cross open from the center of the dough to create a rough square. Dust flour on top and roll dough to 11-inches square.
Remove butter block from refrigerator and peel off parchment paper. Place block onto dough at angle so the corners point to the center of dough sides. Bring the dough up over the butter and pinch the seams together.
First Turn: Roll dough/butter out to a rectangle 1/2-inch thick. Fold the rectangle into thirds like a business letter. Wrap in plastic wrap and refrigerate for 1 hour.
Turns Two–Five: Remove dough from refrigerator and lay horizontally on a flour-dusted work surface. Roll out to a rectangle 1/2-inch thick. Fold the rectangle into thirds like a business letter as before. Wrap in plastic wrap and refrigerate for 1 hour. Repeat until a total of 5 turns have been completed.
To make pastry cases, line two baking sheets with parchment paper. Cut off 2/3 of the dough and roll it out 1/2-inch thick on a floured surface.
Use a 3 1/2-inch round cutter to cut out twelve dough circles. Use a 3-inch cutter to cut out centers, making thin rings. Set the rings aside on a sheet of parchment paper.
Roll out the remaining centers one by one very thin (use flour as needed). Use the 3 1/2-inch cutters to cut out new circles from the rolled-out centers. Prick holes in these circles with a fork and lay them on the prepared baking sheets, six circles to a sheet.
Brush edges with water and carefully attach rings to the edges to form cases. Refrigerate the cases for 1 hour.
Preheat oven to 400°F.
Remove one baking sheet from the refrigerator and line inside each case with small pieces of aluminum foil. Fill foil with beans or pie weights. Bake for 10 minutes. Reduce the heat to 375°F and bake another 20 minutes until the dough is set. Remove the foil and weights and bake another 3–5 minutes until light golden brown.
Raise the heat to 400°F and repeat with the second sheet.
Cool completely on a wire rack before filling.