In a small sauce pan, melt butter over low heat. Once butter is completely melted, remove from heat and add in chopped chocolate. Let chocolate melt into butter, stirring occasionally.
In a small bowl, whisk together flour, cocoa powder, baking powder and salt. Set aside.
Pour butter mixture into bowl of a stand mixer fitted with paddle attachment. Or, into a medium mixing bowl, if using an electric hand mixer.
Add sugars and vanilla to butter and chocolate mixture, beating on low speed until combined (about 2 - 3 minutes), then add egg and beat until completely incorporated.
Add in flour mixture on low speed and mix until just combined. Turn mixer off, scrape down sides and bottom of bowl, then add chips.
Beat on low speed just until chips are evenly distributed in dough. (They may not mix in entirely, this is ok.)
Using a small (3/4 oz. // 1.5 tbsp.) scoop, portion dough onto parchment lined sheet pan. Cover and let rest for 30 minutes in the refrigerator prior to baking.
Preheat oven to 350°F (325° with convection fan) // 180°C // Gas mark 4
Place dough 2 - 3 inches apart on baking sheet lined with nonstick mat (Silpat) or parchment paper.
Bake for 10 - 14 minutes, rotating tray halfway through baking time.
If desired, place a few chocolate chips on top of cookies as soon as they come out of the oven.