1. In a bowl, mix 1 cup flour and the brown sugar. With a pastry blender or fingers, cut or rub in butter to make fine crumbs. Add 1 tablespoon water and stir with a fork until evenly moistened.
2. Gather dough into a ball.
3. On a lightly floured board, roll dough into an 11-inch round. Ease dough into a 9-inch tart pan with a removable rim; if dough tears, overlap edges slightly and press to seal. Gently press dough against bottom and side of pan. Fold excess dough down and flush with pan rim; press against pan side.
4. Bake crust in a 325° oven until golden brown, about 20 minutes. Cool on a rack.
5. In a bowl with a mixer, beat mascarpone, yogurt cheese, lemon peel, mint, powdered sugar, and vanilla until smooth. Spread evenly in crust.
6. Arrange berries in a single layer over filling.
7. In a 1- to 1 1/2-quart pan over medium heat, stir jam until melted, 2 to 3 minutes. Drizzle over berries.
8. Remove pan rim and cut tart into wedges.