Preheat oven to 350ºF degrees and line a baking sheet with parchment paper.
In a mixing bowl, combine the cake mix, baking powder, eggs, yogurt, and vanilla. Stir until smooth and fully incorporated.
Using a small cookie scoop (or two spoons), drop mounds of dough (about the size of a golfball) onto the prepared baking sheet, spacing them 2 inches apart. Dip fingers in a small bowl of water and even out any jagged/uneven edges, if desired.
Bake 8-9 minutes - do not let the cookies brown. The tops should look "dry" and puffed up. Allow cookies to cool on baking sheet for 5 minutes, before transferring to a cooling rack. Use your fingers to gently press the tops down if they don't sink as much as they cool.
Once cookies have cooled completely, line a baking sheet with wax paper. Melt the semi-sweet chocolate until smooth and silky. Carefully dunk one half of the cookie into the chocolate, using a spoon or spatula to skim off any excess chocolate. Place cookie on wax paper-lined baking sheet. Use the same process when dipping in white chocolate. Store cookies in an airtight container at room temperature for up to one week.