Preheat oven to 350 degrees. Melt butter and chocolate together in a metal bowl over simmering water. Remove from over water and set aside. In a large bowl, whisk together sugar, eggs and vanilla. Whisk only to blend. Add chocolate mixture and whisk gently. Add flour and salt and use the whisk to stir in until blended. Grease a 12 by 12-inch square pan, and line the bottom with parchment. Pour a scant half of the brownie batter into pan and spread smooth. Place the 16 peanut butter cups upside-down onto the batter, spacing them evenly in 4 rows of 4 (the brownies will be cut into 16 squares, with a peanut butter cup in the center of each.) Push the cups down into the batter slightly. Top with the remaining batter and gently spread smooth. Bake 30 minutes. Center will still be soft. Remove from oven and let cool in pan on wire rack. Cool completely before cutting, or for best cutting results, chill several hours or overnight in refrigerator. Cut into 16 (3-inch) squares.