Sift the flour, cocoa powder, baking soda and salt into a medium-sized bowl (2-3 quarts).
Using a stand mixer or a medium-sized mixing bowl (2-3 quarts) and a handheld mixer on medium-high speed, beat the peanut butter and butter together for 1-1½ minutes until smooth.
Add the dark brown sugar and continue mixing for another 1-1½ minutes until combined.
Lower the mixer speed to medium-low. Add the egg and beat just until there are no more yellow streaks.
Add the vanilla and mix just until no brown streaks from the vanilla remain.
Keep the mixer speed on medium-low, and add the flour mixture 1 cup at a time, mixing just until incorporated. (Be careful not to overmix the cookie dough, as that can cause the baked cookies to have a tough texture) Cover and chill in the refrigerator for 30 minutes.
Preheat the oven to 350°F. Line 2 baking sheets with parchment paper or heavy-duty aluminum foil. (If you are using aluminum foil, be sure to lightly spray with nonstick cooking spray.)
Add the granulated sugar to a small bowl. Add the sifted powdered sugar to a small bowl or a quart-size ziplock baggie.
Use a 1-tablespoon cookie scoop to scoop out the cookie dough. Roll the cookie dough into a ball. Flatten the cookie dough ball slightly. Place 1 of the miniature peanut butter cup halves in the center. Fold the edges of the dough up and roll the cookie dough and peanut butter cup half into a ball. Roll out all the Reese’s filled cookie balls and place them on one of your cookie sheets.
Now you will roll each cookie dough ball in the granulated sugar first and then roll it in the powdered sugar until completely coated. Place the coated dough ball on the other prepared baking sheet. Space the dough balls 2 inches apart. Do this process (granulated sugar then powdered sugar) to all the dough balls.
Bake for 8-10 minutes or until the cookie surface is crackled. (Every oven cooks differently, but 9 minutes was spot on for me) Allow the cookies to rest on the baking sheets for 2-3 minutes before transferring to a cooling rack to cool completely.
Letting your cookie dough chill will help to prevent your cookies from spreading too much and becoming flat when baking.
Instead of hitting your sifter against your hand to sift the ingredients through you can use a whisk to "stir" the dry ingredients in the sifter basket as they go through. It is a lot less messy since you're not shaking anything.
Oven temperatures vary and may need to be recalibrated periodically to ensure they are accurate. Make sure to check your cookies at the lower end of the recommended baking time.