1. Preheat oven to 350ºF. Line bottom and sides of an 8-inch square pan with parchment paper, allowing about an inch of paper to extend over opposite sides of pan; lightly coat with cooking spray.
2. In a microwave-safe bowl, microwave butter and 1 ⅓ cups chocolate baking chips on medium (50% power) for 2 minutes, stirring every 30 seconds , until melted and combined, about 2 minutes total.
3. Whisk in sugar (mixture will look grainy). Whisk in eggs and vanilla, mixing until smooth.
4. In a separate bowl whisk together cocoa, flour, baking powder, and salt. Stir flour mixture into chocolate mixture until just combined.
5. Fold in half of peppermint bark. Pour mixture into prepared pan; smooth top.
6. Bake, rotating pan halfway through, until a toothpick inserted in center comes out with a few crumbs, 25 to 30 minutes. Let cool on a wire rack for 30 minutes. Lift brownies from pan using parchment as handles and transfer brownies to rack to cool completely.
7. Place brownies on a cooling rack set over a rimmed baking sheet.
8. Place remaining ⅓ cup chocolate baking chips in a medium glass bowl. Warm cream in a small, heavy saucepan over medium-high heat, stirring occasionally, until steaming, 2 to 3 minutes. Remove from heat and pour over chocolate baking chips. Let stand for 2 minutes; whisk until smooth. Pour over brownies and spread to edges with a small offset spatula.
9. Sprinkle evenly with remaining peppermint bark. Before serving, let stand, or refrigerate, until glaze sets.