Preheat oven to 375 degrees F and butter 8 (1/2-cup) muffin cups.
Melt 4 tablespoons butter and cool. In a shallow baking pan toast pistachios in middle of oven, shaking pan occasionally, until golden, about 10 minutes. Cool nuts and finely chop.
On a work surface stack 3 phyllo sheets and cut out 4 (6-inch) squares (for a total of 12 single-sheet squares), discarding scraps. Repeat with other 3 phyllo sheets.
Stack phyllo squares between 2 sheets of waxed paper and cover with a kitchen towel. Line each buttered muffin cup with 1 phyllo square, pressing into bottom (don?t worry if pastry rips). Fold in pastry overhang, brush inside and edges with some melted butter.
In a small bowl, stir together 2 tablespoons nuts and 2 tablespoons brown sugar. Sprinkle bottom of each pastry shell with 1/2 teaspoon nut-sugar mixture. Make 2 more layers of phyllo, butter, nuts, and sugar in same manner. Bake shells in middle of oven until golden brown, about 10 minutes. Carefully lift shells out of pan and transfer to a rack to cool slightly.
While shells are baking, cut peach into 1/2-inch-thick wedges and halve wedges crosswise. In a bowl toss peach and berries with honey, lemon juice, and vanilla and let stand at room temperature, stirring occasionally, at least 15 minutes.
In a small bowl stir together sour cream and remaining brown sugar, to taste. Just before serving, divide sour-cream mixture among shells and with a slotted spoon fill shells with fruit. Drizzle fruit and serving plates with some of remaining fruit juices in bowl. Sprinkle remaining nuts over tartlets.