Preheat oven to 375°F (190°C). Line baking sheets with parchment paper or silicone liners.
Whisk together the flour, cocoa, baking soda, and salt. Set aside.
Using an electric hand mixer or stand mixer on medium speed, beat the sugar, brown sugar, butter, and peanut butter until light and fluffy. Add the vanilla, egg, and water, and mix well.
With the mixer on low speed, gradually add the flour mixture, mixing just until combined. Fold in the peanut butter cups.
Drop the dough by tablespoonfuls onto the prepared pans. Flatten each cookie to about 1/2-inch thick.
Bake one pan at a time for 7 to 9 minutes, or until the cookies are set.
Cool the cookies on the pan on a wire rack for 5 minutes. Then transfer the cookies directly onto a wire rack to cool completely.