Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone liners.
Place the chopped chocolate and butter in a microwave-safe bowl, and heat at half-power in 30-second increments until almost melted. Set aside to cool slightly.
Whisk together the flour, baking powder, and salt.
In a separate bowl, beat the eggs, brown sugar, and vanilla at high speed with an electric mixer. Mix until light and fluffy.
Reduce the mixer speed to low. Beat in the melted chocolate mixture. Then mix in the flour mixture until just combined. Stir in the chocolate chunks. (The dough will be more like brownie batter than cookie dough.) If you like, chill the dough for about 30 minutes.*
Drop the dough by heaping tablespoonfuls onto the prepared pans, leaving 2-3 inches between the cookies. Bake, one pan at a time, 12 to 15 minutes, or until the cookies are shiny and crackly but soft in the center. Be sure not to over-bake.
Cool on the pan on a wire rack for 10 minutes. Then, transfer the cookies from the pan onto a wire rack to cool completely.
Notes
*Some readers say they have the best results chilling the dough briefly before baking. About half an hour of chilling time can help the cookies keep their shape during baking.
The cookies will keep in an airtight container at room temperature up to 3 days.