Partially freeze tenderloins; trim fat from tenderloins. Cut tenderloins diagonally across grain into 1/4-inch-thick slices.
Coat a large nonstick skillet with cooking spray. Place over medium-high heat until hot. Add half of pork, and cook 3 minutes on each side or until pork is lightly browned. Remove pork from skillet. Drain; set aside, and keep warm. Repeat procedure with remaining pork slices. Wipe drippings from skillet with a paper towel.
Combine peach nectar and next 3 ingredients in skillet. Return pork to skillet. Bring to a boil; cover, reduce heat, and simmer 4 to 5 minutes or until pork is tender.
Transfer pork to a serving platter, using a slotted spoon. Set aside, and keep warm. Combine cornstarch and water; stir until smooth. Add cornstarch mixture and chutney to peach nectar mixture; stir well. Add peaches and sliced green onions. Bring to a boil; reduce heat, and simmer, stirring constantly, until thickened. Spoon peach mixture over pork. Garnish with green onion curls, if desired.