Make the chocolate cookie dough. Cream 1/2 cup butter and sugars together with a mixer on medium-high speed for about 3 minutes until light and fluffy. Add 1 egg and 1 teaspoon vanilla extract, then beat on high speed until combined. In a separate bowl, whisk 1 cup flour, 2/3 cup cocoa powder, 1 teaspoon baking soda, and 1/8 teaspoon salt together. With the mixer on low speed, slowly pour into the wet ingredients and beat until combined. Switch to high speed and beat in 1 Tablespoon milk. The dough will be sticky.
Make the peanut butter dough. Cream 1/2 cup butter and sugars together with a mixer on medium-high speed for about 3 minutes until light and fluffy. Add 1 egg and beat on high speed until combined. Add 1/2 cup peanut butter and 1 teaspoon vanilla extract and beat until combined. With the mixer on low speed, slowly add 1 cup flour, 1 teaspoon baking soda, and 1/8 teaspoon salt. Once combined, beat in 1 cup chocolate chips.
Cover both cookie doughs tightly and chill in the refrigerator for at least 3 hours or up to 3 days. This chilling is imperative to prevent spreading and make the dough easier to work with.
Preheat oven to 350°F (177°C). Line large baking sheets with parchment paper or silicone baking mats. Set aside.
Measure about 2 Tablespoons (40g) of chocolate cookie dough and roll into a ball. Measure about 2 Tablespoons (40g) of peanut butter cookie dough and roll into a ball. Press the 2 balls together between your hands and roll them into 1 large ball. Repeat for each cookie, wiping hands clean after every few balls due to the sticky chocolate dough.
Bake the cookies for 12–14 minutes or until the edges appear set and the centers still look soft. If they aren't spreading by minute 9, remove them from the oven and lightly bang the baking sheet on the counter 2–3 times to initiate spreading, then return to the oven to continue baking.