Place the unsweetened chocolate, bittersweet chocolate chips and butter in a large heatproof bowl and set over a saucepan of simmering water, stirring frequently until melted. Remove the bowl from the pan and set aside to cool slightly.
Beat the eggs and sugar in a large bowl with electric mixer at medium-high until thick and pale, about 4 minutes. Add the vanilla. Reduce the speed to low and add the chocolate mixture and mix until throughly combined, about 1 minute.
Whisk the coconut flour, arrowroot, baking powder, and sea salt in a small bowl. Fold the flour mixture and chocolate chips into the batter. Cover the bowl and let stand at room temperature for 30 minutes. The dough will look more like a thick brownie batter at this point.
Preheat the oven to 350ºF and adjust the rack to the middle position. Line a cookie sheet with unbleached parchment paper. Spoon a heaping 1 tablespoon portion of batter per cookie and give about 1 1/2 inches space in-between each cookie. Bake for 11 minutes. Cool and serve.