Position racks in upper and lower thirds of oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper and coat the paper with cooking spray.

Coarsely chop 3 ounces of chocolate and place it in a small microwave-safe bowl. (Alternatively, see Tip.) Microwave on Medium for 1 minute. Stir, then continue microwaving on Medium, stirring every 20 seconds, until mostly melted. Stir until the remaining chocolate melts completely.

Chop the remaining 2 ounces chocolate into pieces the size of mini chocolate chips. Combine in a small bowl with cocoa and cocoa nibs (if using).

Combine egg whites and cream of tartar in a clean medium mixing bowl. Beat with an electric mixer on low for 30 seconds, then at medium speed until soft peaks start to form. Immediately add about 2 tablespoons sugar; beat for 1 minute. Slowly, about a tablespoon at a time, add the remaining sugar, then vanilla, continuing to beat on medium speed until the mixture is smooth, opaque, glossy and thickened, about 2 minutes longer. Scrape down the sides of the bowl, raise the speed to high, and beat for 30 seconds more. Lightly fold in the chocolate-cocoa mixture and the melted chocolate just until evenly incorporated and no streaks remain; do not overmix. Immediately drop the batter by rounded teaspoonfuls about 1 inch apart onto the prepared baking sheets.

Bake the cookies, switching the pans back to front and top to bottom halfway through, until just firm when gently pressed on top but still soft inside, 8 to 12 minutes. Transfer the pans to wire racks and let stand for 1 to 2 minutes. Then slide the paper from the pans to a flat surface and let the cookies cool completely, about 15 minutes. Gently lift the cookies from the parchment paper using a wide-bladed spatula.