Preheat oven to 350°F. Spray an 8x8-inch baking dish with non-stick cooking spray and line with parchment paper.
Melt the butter in a saucepan over medium heat. Turn off heat and whisk in half of the chocolate chips until smooth. Let cool slightly.
Mix the wet ingredients. In a large bowl, stir together the melted chocolate mixture, granulated sugar, brown sugar, eggs, and vanilla extract.
Whisk the dry ingredients. In a separate bowl, combine flour, cocoa powder, and salt. Gradually fold into the wet mixture.
Add chocolate chips. Gently fold in the remaining chocolate chips.
Swirl in peanut butter. Pour the batter into the baking dish. Melt the peanut butter in the microwave for 20-30 seconds, then drizzle over the batter. Use a butter knife to swirl.
Bake for 40-50 minutes. Brownies are done when a toothpick inserted into the center comes out with a few moist crumbs.
Cool completely before slicing.