Soak dried tomatoes in enough hot water to cover for 10 minutes. Drain and chop tomatoes. Meanwhile, remove and discard skin from chicken. Pull meat from bones, discarding bones. Shred meat, reserving 3 cups. Cover and chill remaining meat for another use.
In a large bowl, combine tomatoes, shredded chicken, cheese, and pecans. Add the 2/3 cup salad dressing, tossing to coat.
Line tortillas with basil leaves. Divide chicken mixture among the tortillas. Fold in sides and roll up tortillas. If desired, wrap in plastic wrap and chill for up to 4 hours. To serve, cut each wrap in half diagonally. If desired, serve with additional dressing for dipping. Makes 6 servings.