Bloom the Yeast - Combine together ½ cup of warm milk, 1 teaspoon white sugar and 1 teaspoon active dry yeast and let it bloom for 5 to 7 minutes.
Combine All Dough Ingredients - In the bowl of a stand mixer, add all-purpose flour, melted butter, white sugar, egg, salt and bloomed yeast mixture. With a spoon or spatula, mix the the ingredients until it becomes a shaggy ball. 2 ¼ Cups (270g) All-Purpose Flour, 2 Tablespoons (28g) Unsalted Butter, 1 Whole Large Egg, ¼ Teaspoon Fine Salt Knead the Dough - Fit your stand mixer with a hook attachment and knead the dough on medium speed for 10 minutes or until it passed the window pane test (see note below). The dough should pull clean from the sides of the bowl, but okay if it stick to the bottom of the bowl. If the dough is sticky, you can gradually add a few teaspoons of flour at a time.
Let Double In Size - Coat your hands with oil and lift the dough out of the bowl and form it into a ball. Then oil your bowl (I use the same one) and place the dough back in. Cover with cling wrap and put in a warm place for 1 hour or until it doubles in size.
Make Pistachio Cream - Meanwhile, make homemade pistachio cream. If using store-bought, proceed to the next step. Make Filling - Cut your thawed kataifi into ¼ inch to ½ inch pieces (6 to 12 mm). Cutting them smaller will make it easier to fit through your piping bag. Melt butter in a large frying pan over medium/low heat, then add the kataifi and stirring constantly, cook until golden and crispy. It should take about 8 to 10 minutes. Transfer the toasted kataifi into a medium bowl, and let cool for 10 minutes, then mix in the pistachio cream. Transfer the filling to a piping bag if you'd like, or you can also just spoon it into the donuts.
Prep Parchment Squares - When the dough has almost doubled in size, cut out 8 or 6, 4x4 inch (10x10 cm) parchment paper squares. Set aside.
Divide the Dough - Gently deflate the dough and transfer to a work surface. Using a kitchen scale, weigh the entire dough and then divide by 8. Each piece weighed about 60 grams for me. Feel free to make 6 large donuts.
Shape the Donuts - Cover your dough balls with plastic wrap or a kitchen towel to prevent them from drying out. Working one dough ball at a time, press it flat to get rid of any air bubbles. Gather and pinch the edges together and then place it on your work surface seam side down. Form your hand into a relaxed “claw” shape and cup it over the ball of dough. Then move your hand in small circular motions, gently dragging the ball along until smooth.
Proof the Donuts - Place donuts onto the parchment paper squares and transfer to a large baking tray. Loosely cover with plastic wrap that has been sprayed with a bit of oil and allow to rise in a warm place for about 45 minutes or until it passes the “poke” test. See note below.
Prep the Oil - With 15 to 20 minutes left of proofing, fill a medium to large sized pot with 2 inches of vegetable shortening or neutral oil such as canola, vegetable, or avocado oil. Clip a thermometer on the side of the pot and heat until it registers between 350ºF (167ºC) and 360ºF (182ºC).
Make Chocolate Glaze - In a small bowl, add powdered sugar, cocoa powder, almond extract and gradually whisk in a little bit of milk until you reach your desired consistency. 1 Cup (113g) Powdered Sugar, 3 Tablespoons (16g) Unsweetened Cocoa Powder (natural or Dutch-process), ¼ Teaspoon Almond Extract, 2 to 3 Tablespoons Milk Prep Toppings if Using - Finely chop your pistachios and melt your milk chocolate. You can transfer to a piping bag or drizzle with a spoon.1 Tablespoon Pistachios, 2 Ounces (56g) Milk Chocolate Additional Prep - Place a large cooling rack over a large baking sheet and line it with paper towels and set aside. Grab all the tools you'll need such a kitchen spider or slotted spoon and tongs for removing the parchment paper.
Fry the Donuts - Once the donuts are proofed and the oil reaches 350ºF (180ºF), carefully place 2 to 3 donuts into the hot oil with the parchment paper. After a few seconds, use tongs and remove the papers. Fry for 45 seconds on each side. Then flip the donuts and fry for an additional 20 seconds on each side. Set a timer! Scoop and drain the donuts well and then transfer to a cooling rack that has been lined with paper towels.
Fill & Dip - If your filling is in a piping bag, snip the tip. Using a small paring knife, create a hole on the side of the donuts and fill them. Finally, dip the tops of the donuts and allow the excess glaze to drip off. Top with ground pistachios and then drizzle with melted milk chocolate if you'd like. Serve immediately and enjoy!