Make the pate brisee: Pulse flour, sugar, and salt in a food processor to combine. Add butter, and process until mixture resembles coarse meal, about 10 seconds. With machine running, slowly add ice water, and process until dough just comes together. Divide dough in half, and shape each into a disk. Wrap each in plastic, and refrigerate at least 1 hour (or up to 2 days).
Preheat oven to 375 degrees. On a lightly floured surface, roll out each disk of dough to a 1/4-inch thickness. Cut out 12 circles using a 4-inch round cutter. Fit each circle into 2 1/2-inch tartlet pan. Trim overhang. Refrigerate shells for at least 30 minutes.
Place tartlet shells on a baking sheet, and line each with a small square of parchment. Fill with pie weights or dried beans, and bake 15 to 20 minutes. Remove parchment and weights, and bake until golden brown, 10 to 15 minutes more. Let tart shells cool on sheet on a wire rack.
Make filling: Whisk cream, confectioners' sugar, and vanilla in a bowl until soft peaks form. Fold in creme fraiche. Fit a pastry bag with a 3/8-inch tip (such as Ateco No. 804), and spoon filling into bag. Pipe into tartlet shells, filling each halfway.
Cut mango crosswise into 1/8-inch-thick slices. Roll 1 slice, and press in the center of tartlet. Using 3 to 4 more, wrap each slice around last to create a rose shape. Garnish with mint leaves before serving.