Preheat the oven to 375°F. Line large baking sheets with parchment paper; you will need 2–3 sheets, or be prepared to bake in batches.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium-low speed until fluffy, about 4 minutes. Add the brown sugar and granulated sugar and mix on high speed for about 3 minutes. With a nonstick spatula, scrape down the sides of the bowl, then mix on low speed to make sure all the sugar and butter are combined. Add the egg and mix on low, then add the vanilla and mix on low until combined.
In a large bowl, whisk together the flour, black cocoa powder, baking soda, and salt to combine. Add one-third of the flour mixture to the mixer bowl with the wet ingredients and mix on low speed for 1 minute. Scrape down the bowl, then add half of the sour cream and half of the boiling water and mix on low until just incorporated. Add half of the remaining flour mixture and mix on low for 1 minute, then scrape down the bowl. Add the remaining sour cream and boiling water and mix on low until just incorporated. Add the remaining flour mixture and mix on low for 1 minute, then scrape down the bowl and mix again until just incorporated.
Using a cookie scoop (about 3 tablespoons), scoop the dough onto the prepared baking sheets, leaving 2 inches between the cookies and 1 inch between the cookies and the edges of the pan. You should be able to fit between 8 and 12 cookies per pan, so depending on how many baking sheets you have, you might have to work in batches.
Bake for 8 to 10 minutes, until the tops look dry, you don’t want to overbake these. Use a toothpick and insert it into the center to see if it comes out clean, like a cake tester if you have one. Remove from the oven and let cool on a wire rack while you bake your next batch of cookies and make the filling.