Preheat the oven to 350 degrees. Heat chopped chocolate and butter in a microwave-safe bowl in 20-second increments, stirring between each, until almost melted; do not overheat. In another bowl, whisk together flour, baking powder, and salt.
In a mixing bowl, beat eggs, brown sugar, and vanilla on high speed until light and fluffy. Reduce speed to low; beat in melted chocolate. Mix in flour mixture until just combined. Stir in chocolate chunks.
Drop heaping tablespoons of dough 2 to 3 inches apart onto baking sheets. Bake, rotating sheets halfway through, until cookies are shiny and crackly yet soft in centers, 12 to 15 minutes. Cool on baking sheets 10 minutes; transfer to a wire rack to cool completely.
Don't worry if the batter seems thin. It should look more like a brownie batter than a cookie dough.