Make the phyllo cups:
Position an oven rack in the middle of the oven; heat the oven to 325°F. Lightly butter six large (10-oz.) Pyrex custard cups, ramekins, or muffin tins.
Combine the butter, honey, and salt in a small saucepan. Cook over medium heat, stirring often, until the butter is melted and the mixture is combined, about 2 minutes.
Clear two large work surfaces (one for the phyllo and another for assembly) and set out a long ruler, a sharp knife or pizza wheel, a pastry brush, and a damp towel. Have the butter mixture and the pistachios ready.
Unwrap the phyllo package and peel off six or seven sheets, laying them flat. (Wrap up the remaining dough, refrigerate it, and save for another use.) Carefully lift up one sheet and lay it flat on the other surface; cover the rest of the dough with the damp towel so it doesn’t dry out. It’s all right if the dough tears slightly, but if it sticks to itself or rips severely, toss it out and use the next sheet. Brush the entire sheet with some of the honey mixture. Sprinkle evenly with 1 Tbs. of the pistachios. Lay a second sheet of dough directly on top of the first and press gently. Brush the sheet with another tablespoon of pistachios evenly over the phyllo. Cover with a third sheet of phyllo and press gently. Brush again with the honey mixture and sprinkle with the remaining pistachios. Top with a fourth and final layer of phyllo and press gently.
Using the knife or pizza wheel (use the ruler for a straight edge), trim the phyllo stack into a 16-1/2x11- inch rectangle. Cut it lengthwise into two 5-1/2-inch-wide strips. Cut the strips crosswise into thirds, so you get six 5-1/2-inch squares. Set the six custard cups on a baking sheet. Gently ease a phyllo square into a cup so the bottom fits snugly and the sides form a cup shape. The sides will be a bit ruffly; don’t worry about making them flush. Repeat with the rest of the phyllo.
Bake until the bottom of the phyllo cups are golden all over (the tips will be paler), 14 to 18 minutes. Let cool completely in the custard cups.
Make the compote:
In a small saucepan, combine the honey, lime zest, lime juice, and salt. Cook over medium heat, stirring frequently, until well combined and smooth, about 1 minute. Set aside to cool slightly.
Cut each peach half into thin (1/4- to 1/2-inch) wedges and then cut crosswise into halves or thirds. Put the peaches and berries in a large bowl. Drizzle the warm honey mixture over the fruit, scraping the pan with a rubber spatula, and gently toss. Use immediately or cover and refirgerate for up to 6 hours.
Assemble the sundaes:
Put the ice cream in the fridge to soften slightly, about 10 minutes. Set the phyllo cups on dessert plates. Stir the compote and spoon some fruit into each shell. Add a scoop of ice cream, spoon on some juices from the compote, and sprinkle with the chopped pistachios. Serve immediately.
You can bake the phyllo cups one day ahead and store them in an airtight container.