Preheat the oven to 350° F. Use the melted butter to grease four removable-bottom, 4-inch round tartlet pans.
Place the pistachios in a food processor and pulse until finely ground but not turned to paste. Remove 1 tablespoon and set aside.
Add the flour, brown sugar and vanilla to the food processor and pulse to form a crumbly mixture. Add the cold butter and pulse just until the mixture starts to clump. Scoop out the mixture onto a work surface and form it into a disk.
Divide the dough into four pieces and press the mixture into the bottom and sides of each of the tartlet pans. Place in the oven on a cookie sheet and bake until lightly browned, about 12 minutes. Remove from the oven and allow to cool.
Mix the mascarpone cheese with the salt and 2 tablespoons of the honey in a small bowl. Spread it in each of the cooled shells.
Toss the peach slices with the remaining 1 tablespoon of honey, and arrange them, overlapping, on the mascarpone. Scatter with the reserved pistachios and garnish with the small mint leaves.