Preheat the oven to 350 degrees F and line two baking sheets with parchment paper.
Fill a small saucepan with an inch of water and bring it to a simmer. Put 1/2 cup unsalted butter, cubed and 8 ounces semi-sweet chocolate, chopped in a heatproof bowl and set the bowl on top of the saucepan, making sure the bottom of the bowl does not touch the water.
Let the butter and chocolate melt, stirring gently now and then. Once melted, set the bowl aside to cool. Leave the saucepan of simmering water on the stove.
In a small bowl, sift together 2/3 cup all-purpose flour, 1/3 cup Dutch-processed cocoa powder, 3/4 teaspoon baking powder, and 1/2 teaspoon salt. Set aside.
In a stand mixer fitted with the paddle attachment, add 3 large eggs, at room temperature, both sugars, and 2 teaspoons vanilla extract. Beat on medium speed until the mixture is pale yellow and thick, about 8 minutes. Test it by lifting the beater and letting the batter fall back into the bowl. When the ribbon sits on the surface for a second or two before sinking in, it has been beaten long enough.
Turn the mixer to the lowest speed and slowly add the melted and cooled chocolate and butter. Mix for one minute, then scrape the sides and bottom of the bowl.
With the mixer still on low, add the dry ingredients and mix until just combined.
Add 1/4 cup semi-sweet chocolate chips and use a spatula to fold them into the batter. The batter will be very thick.
Immediately scoop the batter onto the prepared baking sheets using a small cookie scoop, about 1 tablespoon each. Leave space between them, since they spread as they bake.
Bake for 10 minutes, or until the tops are shiny and cracked and the edges are just set.
Cool the cookies on the sheet pan for 10 minutes, then move them to a wire rack to cool completely.
If the cookies need to be baked in batches, set the mixing bowl back over the saucepan of simmering water between trays. Warm batter is what produces the shiny, cracked tops.