In a small bowl, combine the warm plant milk with the yeast and 1 teaspoon of the granulated sugar. Stir briefly and allow the mixture to stand for 5–10 minutes, or until it becomes frothy.

In a large mixing bowl, whisk together the flour, remaining sugar, and salt. Add the activated yeast mixture, melted vegan butter, and vanilla extract. Mix until the dough begins to form, then transfer it to a lightly floured surface and knead for 8–10 minutes, or until smooth and elastic.

Place the dough in a lightly greased bowl, cover it with a clean towel, and allow it to rise in a warm environment for approximately 1 hour, or until doubled in size.

While the dough is rising, prepare the cream filling. Blend the pistachios with ½ cup of plant milk until the mixture is smooth.

In a medium saucepan, whisk together the pistachio mixture, remaining plant milk, maple syrup, cornstarch, vanilla extract, and a pinch of turmeric if desired. Cook over medium heat, whisking continuously, until the mixture thickens to a custard-like consistency (approximately 5–7 minutes). Remove from heat, allow it to cool completely, then refrigerate until needed.

Once the dough has risen, punch it down gently. Transfer it to a floured surface and roll it out to a ½-inch thickness. Using a donut or biscuit cutter approximately 3 inches in diameter, cut out circles of dough.

Arrange the dough portions onto parchment-lined trays, cover lightly, and allow them to rise a second time for 30–40 minutes.

Heat oil in a deep pot to 350°F (175°C). Fry the donuts in small batches for 1–2 minutes per side, or until golden brown. Transfer to a paper towel-lined tray to absorb excess oil, then roll the donuts in granulated sugar while still warm.

Place the chilled pistachio pastry cream into a piping bag fitted with a small round tip. Using a skewer or similar tool, make a small opening in the side of each donut. Insert the piping tip and fill each donut generously with the pastry cream.

Serve immediately or refrigerate until ready to enjoy.