1. Preheat the oven to 350°F and line an 8×8-inch baking pan with parchment paper.
2. In a saucepan, melt the butter over low heat. Remove from heat and stir in half of the chocolate chips until smooth and melted. Let it cool slightly.
3. In a separate bowl, sift together the flour, cocoa powder, and salt.
4. In a large mixing bowl, combine the granulated sugar, brown sugar, eggs, and vanilla extract. Beat them together until well-mixed.
5. Gradually stir in the melted chocolate mixture into the egg mixture until combined.
6. Gently fold the dry ingredients into the wet mixture, and then add the remaining chocolate chips.
7. Pour the brownie batter into the prepared baking pan. Drop peanut butter in teaspoonfuls over the batter and use a knife to gently swirl it through the top layer of the batter.
8. Bake for 40 to 45 minutes, checking for doneness with a toothpick. Cover with foil if the peanut butter swirls start to brown too quickly.
9. Allow the brownies to cool completely in the pan before slicing for best results.