Preheat oven to 225°F. Line 2 large rimmed cookie sheets with parchment paper.
Place egg whites in a clean dry bowl and beat with an electric mixer on medium-high speed until foamy. Add cream of tartar, increase speed to high and whip until mixture forms soft peaks. Gradually add granulated sugar and continue beating until whites are stiff and shiny.
In a separate bowl, sift confectioners' sugar with cocoa to blend. Working in thirds, sprinkle cocoa mixture over egg whites and gently fold in until thoroughly incorporated. Transfer to a large ziplock bag. Seal bag, pinching out excess air. Snip off a small piece of one bottom corner of bag. Pipe out meringues through hole onto cookie sheets, forming small "kisses," about 2 inches in diameter. Bake for 1 hour, until meringues are firm and dry. Turn oven off and let meringues sit in oven for 15 minutes.
Let meringues cool on sheets on wire racks, then gently peel kisses off parchment paper. Store at room temperature in an airtight container.