Preheat Oven: Preheat your oven to 400°F (200°C). Grease a 9x13-inch baking pan.
Mix Dry Ingredients: In a large mixing bowl, whisk together the flour, baking powder, salt, and granulated sugar.
Cut in Butter: Add the cold, cubed butter to the flour mixture. Use a pastry cutter or your fingers to mix until the mixture resembles coarse crumbs.
Add Milk: Pour in the milk and stir until just combined. Do not overmix.
Prepare the Filling:
Make the Filling: In a small bowl, mix the crushed cookies, softened butter, granulated sugar, and vanilla extract until well combined.
Assemble the Rolls:
Roll Out the Dough: On a lightly floured surface, roll the dough into a rectangle, about 1/4 inch thick.
Spread the Filling: Evenly spread the cookie filling over the rolled-out dough.
Roll Up: Starting from one long side, carefully roll the dough into a tight log. Pinch the seams to seal.
Slice the Rolls: Cut the log into 12 equal slices and place them in the prepared baking pan.
Bake the Rolls:
Bake: Bake in the preheated oven for 15-20 minutes, or until the rolls are lightly golden and cooked through.
Prepare the Frosting:
Make the Frosting: In a bowl, whisk together the powdered sugar, cocoa powder, milk, and vanilla extract until smooth. Adjust the consistency with more milk or powdered sugar if needed.
Serve:
Frost the Rolls: Once the rolls are out of the oven, let them cool slightly before drizzling the frosting over the top.