Recipe testing for cookbooks has taught me a few things, and this is one of those things. Before this year, I had no idea that peeling pistachios was an option. I didn’t know how it was done, nor that the method is different for pistachios than it is for hazelnuts (not that I can eat hazelnuts, but I still at least know how to peel those).
To remove the skins/peel of hazelnuts, usually you toast them in the oven, then pour them onto a kitchen towel, cover them, and then rub them like mad. The peel rubs right off into the kitchen towel. Pistachio skins tend to be a little clingier, so the method is different.
To peel pistachios and remove their skins, heat a large pot of boiling water and drop them in when the water comes to a rolling boil. Let the pistachios boil for about a minute or so, at which point you will notice the peels lifting off. Strain out the nuts and drop them into an ice bath immediately to chill them. The goal here is not to boil the pistachios til they are mushy, after all. When the pistachios are thoroughly chilled, the peels should just lift off. This is a slow, tedious task. I suggest you peel them while watching Netflix. You can also rub the blanched pistachios in a kitchen towel to loosen the skins, and then the skins might just rinse off at that point. How you choose to get the peel off in the end is your choice, but the point: to skin a hazelnut, you toast it, but to skin a pistachio, you blanch it.
I let the peeled pistachios air dry on sheets of paper towel, and I use them within a day.