Preheat the oven to 375°F and line two baking sheets with parchment paper.
In a large bowl, cream together the butter, peanut butter, brown sugar, milk, and vanilla until the mixture is smooth. Add the egg and mix just until combined.
In another bowl, combine the flour, cocoa powder, salt, and baking soda by whisking them together.
Slowly add the dry ingredients to the wet mixture and stir until just incorporated.
Place rounded tablespoons of dough on the baking sheets, spacing them about 2 inches apart. Gently press each cookie with a fork to create a crisscross pattern, then sprinkle granulated sugar on top.
Bake the cookies for 6 to 8 minutes until set. Do not overbake to keep them soft. Let the cookies cool on the baking sheet for about 2 minutes before transferring them to a wire rack to cool completely.