Combine butter, milk, sugar, chocolate and sugar in a large bowl. Microwave for 30 second intervals at full power (it takes about 1-2 minutes).
Add the cocoa powder, all-purpose flour, baking powder, salt, and vanilla extract to the batter, and mix until it just comes together. A few crumbs are okay (do not over beat). Fold in the chocolate chips.
Scoop out 1-2 tablespoonfuls of dough with a cookie scoop (or small ice cream scoop), and place on prepared baking sheets. Press them down as thick or thin as you want your cookies to come out.
Bake in a heated oven for 9-11 minutes. The cookies will come out soft from the oven but will harden as they cool. (Be careful not to over bake as they will dry out.) Allow to cool on the cookie sheet for 10 minutes before transferring to wire racks to cool.