Transfer 1 pint of frozen yogurt from freezer to refrigerator to soften for 30 to 40 minutes.

Preheat oven to 375°F. Bake pie crust until lightly browned and crisp, about 10 minutes. Set aside to cool.

To assemble pie, spread softened yogurt evenly over pie crust. Place in freezer and chill about 1 hour. When firm, spread about 3/4 cup caramel evenly over frozen yogurt.

Return pie to the freezer, and transfer second pint of frozen yogurt to refrigerator. Allow pint to soften for 30 to 40 minutes.

Spread second pint of yogurt evenly over caramel, making decorative swirls, if possible. Freeze until firm. Remove from freezer 10 minutes before serving.

To grill peaches, prepare medium fire in a charcoal grill or preheat gas grill on medium. Melt butter and stir in brown sugar until dissolved. Toss peaches with butter mixture until well coated.

Grill peaches directly over medium fire, cut-side up, until grill marks are visible, about 5 minutes. Turn peaches over and grill until grill marks show and peaches are tender, about 4 minutes longer. Set aside to cool. When cool, cut peaches into thick wedges.

When ready to serve, cut pie into wedges and serve with peaches on the side. Drizzle a little of remaining caramel sauce over top.