Heat the oven to 350°F. Line two baking sheets with parchment or foil.
Stir together the flour, baking powder, cardamom, and salt; set the mixture aside.
Put the chocolate and butter in a microwaveable bowl or 2-cup glass measure. Microwave on medium just until the chocolate can be stirred smooth, 1 to 2 minutes, stopping to stir every 15 seconds after the first minute. Stir until smooth, and set the mixture aside.
In a medium bowl, beat the eggs with an electric mixer on high speed until pale yellow and creamy-looking, 2 minutes. Add the sugar and beat until the batter takes on air, thickens slightly, and forms a ribbon when the beaters are lifted, 4 minutes. Beat in the vanilla extract.
Beat in the melted chocolate on low speed just until smooth. Stir in the flour mixture just until blended. Stir in the pistachios.
Drop the dough by rounded teaspoonfuls about 1½ inches apart on the prepared baking sheets. Bake the cookies until the tops are firm to the touch and just beginning to brown but the centers are still moist, 10 to 12 minutes. Cool them on the sheets for 1 minute. Transfer them to racks to cool completely.
Tip: Sicilian pistachios are dark green and come without skins. If you can’t find them, use pre-shelled Californian pistachios. To remove their brown skins, boil the nuts for 30 seconds and then rub off the skins in a clean kitchen towel. Pine nuts or macadamia nuts can also replace the pistachios in this recipe.