Preheat oven to 350 degrees F. Place the tart shells on a baking sheet. Prick the bottom of each tart a few times with a fork. Bake tarts 10 minutes. Remove from oven.
Place the eggs in a bowl and beat until whites and yolks are well combined. Whisk in sour cream, brown sugar and vanilla. Pour the mixture into the tarts shells, filling them right to the top. Bake the tarts 15 to 20 minutes, or until filling is set. Cool tarts to room temperature and refrigerate until needed. (Tarts can be made to this point up to a day in advance.)
When ready to serve, carefully remove the tarts, foil liners. Set the tarts on a platter and top with the berries. Dust with icing sugar and serve.
Recipe Options: Instead of using a mix of berries, simply top these tarts with one type of berry, such as raspberries or blueberries. For a glazed look, don't dust the tarts with icing sugar; brush them with melted strawberry jelly. If you do, you'll need about a half cup of jelly. After you have glazed the tarts, chill them in the refrigerator a few minutes, or until the jelly is set again.