In medium saucepan cook onion in butter until tender. Stir in apricots, stuffing mix, 1/2 cup water and pecans.
Preheat oven to 425°F. Trim fat from meat. Make a cut lengthwise down tenderloins, cutting to within 1/2 inch of opposite side. Spread open; cover surface with plastic wrap. Pound with flat side of meat mallet to 1/2-inch thickness. Remove plastic wrap.
Spoon half the fruit mixture over each tenderloin. Working from long sides, roll up tenderloins to cover stuffing. Tuck in ends. Tie at 1-inch intervals with cotton kitchen twine.
Place tenderloins on rack in shallow roasting pan. Rub with thyme and black pepper to taste. Roast 30 to 35 minutes or until meat and stuffing reach 160°F. Remove twine; slice and serve.
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