Place chocolate in a large microwave-safe bowl and microwave on 50% power for 2-3 minutes, until 80% melted. Add butter and stir until chocolate and butter are both melted. Stir in sugar and vanilla extract. Slowly add eggs, whisking constantly with a fork until combined.
In a separate bowl, whisk together flour, baking powder and salt. Add to chocolate mixture and stir to combine. Stir in three-quarters of the chopped white chocolate. Chill dough 30 minutes (or overnight).
Preheat oven to 375ºF. Form dough into 2" balls. Press a white chocolate chunk into the top of each cookie ball and place 2" apart on parchment-lined baking sheets. Bake 7-9 minutes, until set at edges and starting to crack but still sof in the centre. Cool a few minutes on baking sheets then transfer to wire racks to cool completely.