Preheat the oven to 135 C / 275 F . Draw 4 10cm circles on 2 pieces of baking paper, flip the paper over and line 2 large baking trays with it. In a small bowl, mix together the sugar, arrowroot starch and salt. Set aside.
Pour the chilled chickpea liquid (aquafaba) into the bowl of a stand mixer fitted with the whisk attachment. Add the apple cider vinegar and beat at low speed, gradually increasing the speed to high. Beat for a few minutes, until the chickpea liquid is fluffy, quadrupled in size and has formed soft peaks. Turn the speed down to medium‐high and start adding the sugar sloooooowly, one tblsp. at a time, continuing until it has all been incorporated.
Once all of the sugar has been added, increase the speed back to high. Continue to beat until stiff, very glossy peaks form and hold their shape. To test if the meringue has been whisked for long enough, remove the bowl from the mixer and turn it upside down, the meringue should stay in place. If not, continue beating until it passes this test. Once it has been properly whisked, stop the mixer and add the vanilla extract, beat for another minute on high until incorporated. Remove the bowl from the mixer and gently fold through the chopped pistachios.
Quickly scoop the meringue into the center of the drawn circles on your prepared baking paper / baking trays. Using a spatula, spread the meringue around to fill the circle, piling it higher around the edge to form a kind of moat for when you add your fillings to the center later. You can use a spoon to create a larger nest in the center if needed (it does puff up quite a bit whilst baking, so create a bigger divet in the middle than you think).
Put the prepared meringues in the oven on the middle rack, and immediately turn the temperature down to 120 C / 250 F. Bake for 2 — 3 hours, or until the outside is dry to the touch and sounds hollow when tapped lightly. Turn the oven off and leave the pavlova inside to cool completely.