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1
Mix together the flour, 3 tablespoons sugar, salt, cinnamon, and cardamom, and chill in the fridge for 30 minutes.
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2
Stir together the yeast and water in a small bowl. In the bowl of a stand mixer fitted with a dough hook (or by hand in a large bowl with a wooden spoon), combine the chilled flour mixture, the eggs, egg yolks, milk and buttermilk. Mix on low speed until a dough forms. It might be a little shaggy on the sides and that's ok.
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3
Add the yeast and continue mixing on low for 3 minutes. Pinch a piece of dough. It should be quite soft and sticky but should begin to stretch. If not, keep kneading for another 2 minutes.
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4
Add the Plugra butter, 1/ 3 at a time, and let the mixer knead for 5 minutes after each addition. The dough should become very smooth and elastic. It will seem impossibly soft, and should feel a little bouncy like a marshmallow. Don't despair. This is right.
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5
Brush a bowl twice the size of the dough mixture with oil. Scrape the dough into the bowl. Lightly brush the top with oil. Cover the bowl with plastic wrap, and let rest at room temperature for 45 minutes.
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6
Using a dough scraper, fold in the sides of the dough (don't punch it down, just fold it). Let rest, covered, for another 45 minutes, then fold it again. Cover and place the dough in the refrigerator overnight (or for at least 8 hours).
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7
Lightly flour a work surface. Line 2 baking sheets with parchment paper. Have your kitchen scale ready (if not you'll be dividing the dough into 9 equal pieces) and a spray bottle filled with water. Spread the chopped pistachios on a small plate. Remove the dough from the bowl and set it onto the floured surface. Using your dough scraper, cut and weigh out 100 g pieces. You should have exactly 9 pieces.
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8
Using as little flour as possible, shape the dough pieces into rolls, and set the rolls on a floured portion of the work surface, at least 5 inches apart. Let rest for 10 minutes. If the dough becomes difficult to handle at any time, put it back in the fridge to chill for 30 minutes.
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9
Get out your 1-and-1/2-inch round cookie cutter. One at a time, firmly pat the rolls into 1/2-inch-thick disks. Cut out the centers with the cookie cutter.
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10
Working one doughnut at a time, spray a doughnut with just enough water to wet its surface. Dip the wet side of the doughnut into the pistachios, and set, nut-side-up, on the parchment-lined baking sheet. Repeat with the remaining doughnuts and doughnut holes, spacing them at least 3 inches apart. Cover loosely with plastic wrap. Let rise until fluffy and light - the doughnut should bounce back when pressed - about 1 1/2 hours.
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11
Heat the oven to 375 degrees. Bake the doughnuts for 6 minutes, then turn the baking sheets from back to front and continue baking until lightly browned and cooked through, 4 to 6 more minutes. Meanwhile, melt the remaining 4 tablespoons butter and place 1 cup sugar in a wide, shallow bowl.
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12
After removing the doughnuts from the oven, again working one at a time, brush the doughnuts with butter, then dip in the sugar, and set on a baking rack to cool.
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13
Pat yourself on the back, and eat while fresh!
