Preheat oven to 350°.
Prepare brownie mix according to package directions, using 2/3 cup yogurt. Pour batter into a foil-lined 8-inch square baking pan coated with cooking spray. Bake at 350° for 34 minutes. Cool completely in pan on a wire rack.
Combine ice cream and peppermint extract in a large bowl; stir well. Spread evenly over brownie. Cover and freeze 8 hours or until firm.
Sprinkle chopped mints over ice cream. Cut into squares; drizzle with chocolate syrup before serving.