Heat oven to 375°F. In small microwavable bowl, place carrots. Cover; microwave on High about 1 minute or until tender. Meanwhile, in medium bowl, gently mix chicken, Swiss cheese, onions, asparagus and spreadable cheese. Stir in carrots.
To make 1 bundle, layer 5 phyllo pastry sheets, generously spraying each layer with cooking spray (sheets can be stacked randomly). Keep remaining pastry sheets covered with damp cloth until needed to prevent dough from drying out. Place about 1/2 cup chicken mixture in center of stack of pastry. With both hands, lift pastry stack towards center and twist in center to make bundle (pastry may tear a little). Spray outside of each bundle generously with cooking spray; place on ungreased large cookie sheet. Repeat to make 7 more bundles.
Bake 20 to 25 minutes or until pastry is browned and crisp.