Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a medium saucepan, melt the semi-sweet chocolate chips and butter over low heat, stirring until smooth. Remove from heat and let cool slightly.
In a large mixing bowl, whisk together the granulated sugar, eggs, and vanilla extract until well combined.
Gradually add the melted chocolate mixture to the sugar mixture, stirring until smooth.
In another bowl, sift together the flour, cocoa powder, salt, and baking powder. Gradually fold the dry ingredients into the chocolate mixture until just combined.
Gently fold in the milk chocolate or white chocolate chips.
Drop tablespoon-sized balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, until the edges are set but the centers are still soft. Do not overbake.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.