Preheat oven to 400 degrees F. Melt butter in a large saucepan over medium heat. Cook onion, celery, flour, rosemary, thyme and pepper, 3 minutes, stirring constantly.
Slowly add broth, stirring until smooth. Cook, stirring constantly, until thickened.
Stir in turkey, peas and carrots and green beans. Spoon into four 10-oz. ramekins.
Cut 4 circles out of puff pastry sheet, using outer edge of ramekin as a guide. Place pastry over turkey mixture in each ramekin. Blend egg and water; brush over pastry. Place ramekins on rimmed baking sheet.
Bake 25 minutes or until golden brown and puffed. Let stand 10 minutes before serving.