1. Preheat oven to 325°. Place cookies in a large zip-top plastic bag; seal bag, and finely crush cookies using a rolling pin (about 2 cups crushed); pour into a large bowl. Stir in melted butter and 2 Tbsp. sugar. Press on bottom and up sides of a 9-inch square tart pan with removable bottom. Place on a baking sheet.
2. Bake crust at 325° for 10 to 12 minutes or until lightly browned. Let cool 10 minutes; freeze 20 minutes or until cold.
3. Meanwhile, let ice cream stand at room temperature 20 minutes or until slightly softened. Spread over cooled crust in pan. Freeze 3 hours or until firm.
4. Toss together blackberries, next 3 ingredients, and remaining 1 Tbsp. sugar in a medium bowl. Let berry mixture and tart stand at room temperature 10 minutes. Remove tart from pan, and place on a serving stand or plate. Top with berry mixture.