Preheat the oven to 350°F and line two baking sheets with parchment paper.

Place the butter and peanut butter in a microwave-safe bowl and microwave in 15 to 20 second bursts, stirring in between, just until softened (not hot or fully melted). Beat in the brown sugar and sugar until creamy, then mix in the eggs one at a time until smooth.

In a separate bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and salt. Add to the wet ingredients and mix until well combined.

Stir in the peanut butter and milk chocolate morsels (and the extra chocolate chips, if using) until evenly dispersed. If the dough feels soft or greasy, cover and chill it for 30 minutes.

Use a 1-inch cookie dough scoop, or shape the dough into 1 to 1 ½ inch balls depending on the size of cookie you want. Place the dough balls about 2 inches apart on the prepared baking sheets and press each one down with a fork (just like peanut butter cookies). The cookies will spread a little.

Bake for 10 to 12 minutes, until the edges look set and the tops are puffed and slightly cracked but the centers still look soft. Let the cookies sit on the baking sheet for 3 to 5 minutes before moving them to a cooling rack.