Heat oven to 400°F. Lightly spray 4 (10-oz) custard cups or ramekins with cooking spray. On lightly floured surface, roll puff pastry to 13-inch square. Cut into 4 squares. Lightly press 1 square in bottom and up sides of each custard cup, letting corners hang over sides.
In 10-inch skillet, melt butter over medium heat. Add shallots. Cook about 3 minutes, stirring occasionally, until shallots are softened. Add chicken, frozen peas and carrots, and Alfredo sauce. Cook 3 to 4 minutes longer, stirring occasionally, until peas are thawed and mixture is hot. Sprinkle with thyme leaves; stir well.
Spoon mixture into pastry-lined custard cups. Fold corners over filling, pinching to almost close tops. In small bowl, beat egg with fork or wire whisk; brush pastry tops with egg.
Bake 25 to 30 minutes or until pastry is deep golden brown. Let stand 5 minutes. Serve in cups, or remove to individual serving plates.