a deep-fry thermometer; a squeeze bottle or piping bag; a 2 1/2-inch round cutter
For the dough: In a medium bowl, combine the milk, water, yeast and 1 teaspoon of the sugar and give it a little stir. Let it sit for about 5 minutes, until it becomes foamy on top.
Meanwhile, in the bowl of stand mixer fitted with a dough hook, mix together the flour, salt, cardamom, cinnamon, orange zest and remaining 1/4 cup sugar. Add the eggs, vanilla and yeast mixture and mix to form a very very stiff dough. It will seem like the dry ingredients aren't all going to get incorporated, but try as best you can. Knead for a few minutes and then with the mixer on, begin gradually adding the butter, tablespoon by tablespoon. This, too, will seem like it isn't going to incorporate into the dough, but keep on mixing for 8 to 10 minutes more, scraping down the dough hook occasionally, until your dough is smooth and slightly sticky. Transfer the dough to an oiled bowl, cover it with plastic wrap and let it sit at room temperature (or in the fridge, see notes) until it has doubled in size, about 2 hours.
Turn the dough out onto a work surface and roll it out to 1/2-inch thickness. Cut out 2 1/2-inch circles and transfer them to a baking sheet lined with parchment. When re-rolling scraps, first press them together and then allow the dough to sit for about 10 minutes before proceeding. Cover the circles with plastic wrap or a dish towel and let rise for another hour, until doubled.
In a large heavy pot fitted with a thermometer, heat 3 to 4 inches oil to 350 degrees F. Fry the donuts in batches of 3 or 4, for 1 1/2 minutes on each side. Transfer to a wire rack to cool.
For the filling: Meanwhile, in a small bowl, combine the jam and rosewater. Taste and adjust as desired. Fill a squeeze bottle or piping bag with the jam.
For the glaze: Whisk together the powdered sugar, milk, vanilla and salt until smooth. It should be the consistency of a slightly thicker glue; if it's too thick, add a little more milk, and if it's too thin, add a little more powdered sugar. Dip the cooled donuts into the glaze and let any excess drip off (if the glaze has a hard time sticking to the donuts, that means it's too thick and that you should add more milk). Stick the squeeze bottle straight down into the center of each donut, wiggle it around to make space and fill up with jam. Top with a sprinkle of pistachios and rose petals and enjoy!