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 1/2 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 pinch the dough around the edges of the peanut butter cup. Try to keep the peanut butter cups horizontal.
Freeze the cookie dough balls for at least 30 minutes or up to 2 months. Ensure they are covered. If freezing for longer than a few hours, be sure to place them in a freezer bag or freezer safe container. If in a freezer safe container, I recommend covering tightly with plastic wrap as well to avoid freezer burn.
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.