Heat the milk in the microwave til it reaches 100 F -110 ℉. Stir in the yeast and 1 tablespoon of sugar til yeast is dissolved. Let stand until foamy, about 5 minutes.*
In the bowl of an electric stand mixer fitted with the hook attachment, add the flour, salt, butter, eggs and 2 tablespoons of granulated sugar.
Once the yeast is foamy, add it to the bowl with the rest of the ingredients. Beat on low until a soft dough forms. Increase the speed to medium and beat for 10-15 more minutes or until the dough passes the windowpane test-*Take a piece of dough about the size of a walnut. Gently stretch it between two hands as far as possible. If it tears easily, kneading it a bit longer. You should be able to spread it to where it’s thin enough to can see light pass through. Once you get to that point, you can stop mixing.
Lightly grease a large mixing bowl with oil or butter and transfer dough to that bowl. Cover bowl with plastic wrap and a kitchen towel. Let dough rise in a draft free place at warm room temperature until doubled in bulk, 1 to 1½ hours. Once it has doubled in size, punch dough down to remove excess air.
Turn dough out onto a well floured surface and roll it out with a rolling pin til dough is 1/2 inch thick. (Lightly flour both your rolling pin and donut cutter). Use a 3 inch donut cutter to cut out as many rounds as possible. Set 12 squares of parchment paper on a baking sheet. Place each donut on a square.
Cover donuts with a clean kitchen towel and let rise in a warm, draft free room at room temperature until they appear slightly puffed, about 30 minutes.
About 15 minutes before the donuts finish rising, add about 3 inches of oil to a heavy-bottomed pot or Dutch oven over medium heat and heat it to 350-355 ℉.
While the oil warms, line a plate with paper towels and take out a slotted spoon or spider strainer. Add the sugar (for coating the fried donuts) to a bowl. If adding lemon zest, zest the lemon into the sugar then rub the lemon zest into the sugar with your fingertips. Set aside. Take out everything else you'll need for frying the donuts and set everything next to your stovetop so you have them handy.
Once the donuts have puffed up, carefully place about 3 donuts with the parchment paper at a time into the pot. Use metal tongs to remove the parchment paper. Fry for around 1 minute or minute and a half on each side, or until golden brown.
Recheck the temperature of the oil periodically as you go, so as not to let the oil get too cool or too hot. Adjust temprature of oil as needed.
Drain on paper towels briefly then roll the donuts in granulated sugar or granulated sugar mixed with lemon zest while donuts are still warm. Set donuts on a wire rack set over a baking sheet. Cool to room temperature before filling them.
To fill donuts, transfer pistachio cream into a pastry bag with a wide tip. Insert the end of a spoon (not the end you eat with) into the side of a donut to create some space for the curd.
Gently squeeze pistachio cream into each donut. Enjoy!
Notes
Pistachio paste: I use storebought pistachio paste (also known as pistachio spread) such as Pistakio or Pisti brandsfor the filling to save time. You can definitely swap in homemade pistachio paste or pistachio cream if you prefer! Yeast: I use active dry yeast in this recipe, but you can use either instant or active dry yeast. If the active dry yeast doesn't activate and get foamy, discard it and start over. If you're using instant yeast, then you don't need to heat the milk or add the yeast to it. Just add all the ingredients to the mixing bowl. Stand mixer: I recommend using a stand mixer fitted with a dough hook attachment. Shaping the donuts: You can shape the donuts by rolling the dough out and cutting it out. Alternatively, instead of rolling out the dough, you can divide the dough into 12 pieces using a bench scraper to cut it. Roll each piece into a ball and place it on the baking sheet to rest. Rolling out the donuts: I don't recommend rolling dough out a second time to use up the remaining dough. Doing so can give you hard donuts. That said, if you do want to use up the remaining dough, gently knead the scraps together only as much as necessary, making sure not to overwork it. Let it rest a few minutes then roll it out and cut our the remaining donuts.Oil temperature: Use a candy thermometer. Keep the oil temperature between 350°F to 355°F while frying.Don't overcrowd pot: Don't try to fry too many donuts at once. If you overcrowd the pot, it's hard to keep the set temperature. For best results, fry 3 donuts at a time.Storage: Fried donuts are definitely best enjoyed the day they are fried. If you wish to store them, store unfilled donuts at room temperature in an airtight container for up to 2 days. Store filled donuts in the fridge for up to 2 days.