Place 1 rack in the upper third and 1 rack in the lower third of the oven and preheat to 350°F (180°C). Line 24 standard muffin cups with paper liners. In a bowl, sift together the flour, cocoa powder, baking powder, baking soda and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat together the sugar, oil, eggs, vanilla and 1/2 cup (125 ml) water on medium speed until combined. Reduce the speed and add the flour mixture in 3 additions, alternating with the sour cream and beginning and ending with the flour, and beat until combined.
Divide the batter among the prepared muffin cups, filling them three-fourths full. (Don’t fill less than three-fourths full because you want the cupcakes to form a dome when baking.) Bake until the tops of the cupcakes have formed a crust but still spring back when lightly touched and a toothpick inserted into the center comes out clean, 20 to 25 minutes, rotating the pans between the racks halfway through baking. Transfer the pans to wire racks and let cool for 10 minutes. Remove the cupcakes from the pans and let cool completely on the racks.
While the cake cools, make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium speed until smooth, about 1 minute. Reduce the speed to low, add the confectioners’ sugar, and beat until combined, stopping the mixer to scrape down the sides of the bowl as needed. Add the salt and vanilla and raise the speed to medium-high. Add the cream cheese about 1 Tbs. at a time until combined and no bits of cream cheese remain, about 2 minutes. Raise the speed to high, add the cream, and beat until combined, 30 to 45 seconds. Add the cookie crumbs and beat until thoroughly combined, about 30 seconds. Transfer the frosting to a large pastry bag fitted with a large closed star tip.
Slice off the cupcake tops right where they meet the paper liners and reserve the cake tops. Pipe a layer of frosting around the outside edge of each cupcake, then cover with a reserved cupcake top. Pipe a dollop of frosting in the center of each cupcake, top with a cookie piece and serve.