Preheat oven to 275°. Line 2 baking sheets with parchment paper.
Bring 2 inches water to a simmer in a saucepan.
Put chocolate in heatproof bowl and set over simmering water. Melt, stirring occasionally. Set aside to cool slightly.
In another bowl, combine egg whites and sugar. Place over simmering water and whisk until hot, 4 to 5 minutes. Transfer bowl to a mixer and beat on high speed until stiff peaks form and mixture is lukewarm, 4 to 5 minutes.
Remove bowl from mixer and drizzle melted chocolate over the egg whites, folding in with a rubber spatula until just marbled.
Use a soup spoon to drop batter in large mounds spaced 1 1/2 to 2 inches apart on the baking sheets.
Bake until crunchy outside and still chewy inside, 35 to 40 minutes.
Transfer pans to a wire rack and cool completely before removing the cookies from the parchment.