1Heat oven to 375°F (350°F for dark or nonstick cookie sheet). In medium bowl, stir cookie mix, 1/2 cup butter, the water and egg until dough forms. Drop dough by tablespoonfuls onto ungreased cookie sheet, making 18 cookies.
2Bake 8 to 10 minutes or until edges are set. Cool 1 minute; remove from cookie sheet to cooling rack. Cool completely.
3Meanwhile, heat gas or charcoal grill. In small bowl, mix brown sugar, cinnamon and 2 tablespoons butter; set aside. Carefully brush oil on grill; place peach haves, cut sides down, on grill over medium-high heat. Cook uncovered about 5 minutes until peaches start to soften. Turn peaches over; spoon brown sugar mixture into centers. Cook 5 minutes longer; remove from grill.
4Place 1 peach half in each of 6 dessert bowls. Top with scoop of frozen yogurt. Divide blackberries among bowls. Crumble 1 molasses cookie over top of each; serve 2 cookies on the side.