Mix 1 cup yogurt and cocoa powder together in a bowl until well combined, then pour onto the parchment paper and spread evenly.
In a separate bowl, combine 1 cup yogurt and protein powder; mix well to combine. Drop dollops over the top of the chocolate yogurt layer. Using a butter knife or wooden skewer, create a swirl pattern with the mixture.
Freeze for at least 3 hours, or until firm.
Cut into 2-inch squares and enjoy immediately. Store portioned yogurt bark in an airtight container in the freezer for up to 5 days.