Preheat your oven to 350°F (175°C). Generously grease two standard 6-cavity donut pans with nonstick spray, making sure to coat all the ridges.
In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, cardamom, and salt until evenly distributed with no clumps.
In a separate medium bowl, whisk together the milk, Greek yogurt, eggs, melted butter, and 1 teaspoon vanilla extract until completely smooth.
Pour the wet ingredients into the dry ingredients and gently fold with a rubber spatula just until combined and no flour streaks remain, being careful not to overmix.
Transfer the batter to a piping bag or large zip-top bag with one corner snipped off. Pipe the batter into the prepared donut cavities, filling each about two-thirds full.
Bake for 12-14 minutes, until the donuts spring back when lightly pressed and a toothpick inserted comes out with just a few moist crumbs. Let cool in the pans for 5 minutes.
Remove the donuts from the pans and transfer to a wire rack set over parchment paper. Allow them to cool for another 5-10 minutes while you make the glaze.
For the glaze, whisk together the powdered sugar, 3 tablespoons milk, and 1/2 teaspoon vanilla extract until smooth. Add the remaining tablespoon of milk if needed to reach a pourable but not-too-thin consistency.
Dip the top of each slightly warm donut into the glaze, letting the excess drip back into the bowl. Immediately sprinkle the chopped pistachios over the wet glaze.
Return the glazed donuts to the wire rack and let the glaze set for 15-20 minutes before serving. The glaze will firm up to a beautiful sheen.
