Heat oven to 375°F. Spray large cookie sheet with cooking spray. Unroll dough on work surface; press into 12x9-inch rectangle. Cut into 12 rectangles.
In 10-inch nonstick skillet, heat oil over medium-high heat until hot. Add turkey; cook 4 to 5 minutes, stirring occasionally, until no longer pink. Stir in water chestnuts, carrot, cilantro, garlic, apricot preserves, soy sauce, ginger and red pepper flakes. Spoon about 1 tablespoon turkey mixture onto long side of each dough rectangle to within 1/4 inch of short ends. Starting with long side, roll up. Pinch edges to seal. Place seam side down on cookie sheet. Brush with egg.
Bake 10 to 15 minutes or until deep golden brown. Remove from cookie sheet.
Meanwhile, in 1-quart saucepan, heat sauce ingredients over low heat, stirring until hot. Remove from heat. Serve with turkey rolls.