Place the 54-percent bittersweet chocolate and unsweetened chocolate in a medium glass mixing bowl and microwave on high for two 30-second intervals, stirring after each interval. If still not smooth, heat for 10 additional seconds at a time and stir until smooth. Set aside to cool to 90 degrees F, approximately 15 minutes.
Whisk the flour, baking powder and salt together, transfer to a paper plate and set aside.
Put the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until combined and looks like wet sand, about 2 minutes.
Whisk the eggs and vanilla together in a small bowl. Turn the mixer on low speed and slowly add the egg mixture until fully incorporated. Pour in the melted chocolate and mix to combine. Stop and scrape down the sides of the bowl.
With the mixer on low speed, add the flour mixture and mix until integrated. Add the 70-percent bittersweet chocolate, 40-percent milk chocolate and the cocoa nibs and mix until combined. Cover the bowl with plastic wrap and refrigerate for 45 minutes.
Preheat the oven to 350 degrees F.
Scoop the dough using a 1 1/4-inch-diameter disher or ice cream scoop onto parchment-lined half-sheet pans, placing 2 inches apart, 12 cookies per pan. Bake for 8 to 9 minutes, rotating after 5 minutes. Do not over-bake; the cookies may look wet and doughy.
Cool the cookies on the pan for 2 minutes, then transfer on the parchment paper to a cooling rack to cool completely.