Whisk together the flour, cocoa, baking soda, baking powder and salt in a medium-sized bowl. If the cocoa is very lumpy, sift it first.
In a separate large bowl, beat together the butter, brown sugar and granulated sugar until creamy.
Beat the egg and vanilla extract into the butter mixture.
Turn off the mixer and scrape down the sides of the bowl. Mix the dry ingredients into the butter mixture about ½ at a time, starting with the mixer on a low speed.
Turn off the mixer and stir in the chocolate chips.
Cover the bowl with plastic wrap and place in the fridge for about 30 minutes.
Scoop out about 1 to 1.5 tablespoons of dough and flatten slightly to create a slight bowl shape.
Place an unwrapped peanut butter cup in the middle of the dough and wrap the dough around the sides of the peanut butter cup.
Scoop a second 1 to 1.5 tablespoons on top of the peanut butter cup.
Flatten the top scoop of dough slightly and roll the dough into a ball shape. Ensure that the peanut butter cup stays horizontal.
Place the cookie dough balls on a plate and cover with plastic wrap. Place in the fridge to chill for at least 3 hours or up to 48 hours.
When ready to bake, preheat the oven to 350F (180C or 160C fan forced). Line baking sheets with parchment paper.
Place the cookies (keeping the peanut butter cup horizontal) on the lined cookie sheets, ensuring that they're at least 2.5 inches apart.
Bake 1 sheet at a time in the preheated oven for 12-14 minutes or until the tops look just set. Optionally, place a few extra chocolate chips on top of each cookie.
Cool the cookies on the cookie sheet for at least 10 minutes, then transfer to a cooling rack to continue cooling.