In a medium bowl, cream the softened butter, sugar, and vanilla together until the mixture looks pale and fluffy—about a minute or two with a hand mixer. Add the flour and salt and mix just until the dry spots disappear. The dough won’t be smooth; it will look crumbly with big clumps. That’s perfect. Fold in the chopped pistachios with a spatula or your hands.

Press the dough together and form it into a log, keeping the ends as flat as you can (this helps the slices bake evenly). Wrap the whole log tightly in plastic wrap and refrigerate it until firm—usually 30 minutes, but closer to an hour if your kitchen is warm.

Heat your oven to 350°F. Unwrap the chilled dough and cut it into 12 slices. The easiest way to get even pieces is to halve the log, cut each half in half again, and then get three slices from each quarter. Transfer the slices to a lined baking sheet.

Bake for 15–18 minutes, or until the edges turn lightly golden. Cool the cookies on the sheet for 10–15 minutes, then move them to a rack. They need to be completely cool—not even slightly warm—before dipping. Plan on about 30–45 minutes total cooling time.

In a small bowl, whisk the powdered sugar to break up any lumps. Stir in the pomegranate juice and lime juice until the glaze looks smooth. Add the cream or milk a tiny bit at a time (start with 1 teaspoon). You’re aiming for a consistency that you can dip a cookie into without it running right off.

When the cookies are fully cooled, dip each one halfway into the glaze and let the extra drip back into the bowl. Set them on parchment, wax paper, or a cooling rack until the glaze firms up.