Before starting, just a note that you want to work quickly while making the dough because we want the hot butter to help melt the chocolate, resulting in a deeper cookie color!
Preheat oven to 350℉.
Cut the stick of unsalted butter (½ cup, i.e. 1 stick) into pieces (about 6-8 is fine). In a small microwave-safe bowl, melt the butter for 45-60 seconds until melted. I recommend covering your bowl with a paper towel because it will splatter! We do want the butter hot, so after it pops once, check on it. If it's still not fully melted, microwave in 5 seconds intervals until totally melted.
Immediately after removing butter from microwave, add light brown sugar (1 cup) and mix on low speed for 10-15 seconds until combined. Mixing the hot butter with the brown sugar will help create the deeper caramely color - this is important!
Add peanut butter (½ cup) and mix for 10-15 seconds on low speed until combined. While the mixer is on low speed, add in eggs (2 large) and vanilla extract (2 teaspoons) followed by the baking soda (½ teaspoon), baking powder (½ teaspoon), and salt (½ teaspoon). Add in all-purpose flour (1 ¼ cups) and mix for 10-15 seconds until all the flour disappears into the dough.
Immediately add the semi-sweet chocolate chunks or chips (1 cup) into the dough and mix on medium speed for 30 seconds. Allow dough to sit for about 5 minutes to slightly set so it's not as sticky. If you want the cookies to be a bit flatter like the photos above, after letting it sit for 5 minutes, turn the mixer back on and beat for 20 seconds on medium speed. This will add a little air back in & also work any melted chocolate into the dough to give it a deeper color - this step is also important for deep-colored, chewy cookies! Line a baking sheet with parchment paper. Scoop dough into 3-tablespoon sized scoops. If desired, press a couple extra chocolate pieces into the tops.
Bake at 350℉ for 10-11 minutes. You want them to be slightly brown on top and look slightly underbaked (my oven was perfect at 10 minutes).
Remove from oven and place entire pan on a cooling rack. If desired, press in a few more chunks to the top. Allow the cookies to cool on the hot pan for 10-15 minutes before removing them. This will allow them to finish baking on the hot pan. Once cooled, use a spatula to transfer them to a wire cooling rack.