Heat oven to 400°. Roll out puff pastry and cut to fit tops (adding a ½-inch allowance around each for anchoring) of six 8-ounce ramekins or other ovenproof serving pieces. Lay dough on a parchment-lined baking sheet and refrigerate until ready to use. In a large saucepot over medium-high heat, melt butter with oil and saute celery, shallot, and carrots 7 to 8 minutes. Add stock, bay leaves, thyme, parsley, and chicken. Lower heat and simmer until chicken is fully cooked, about 15 minutes. Remove chicken and set aside to cool. Raise heat to high and boil until liquid is reduced by half, about 15 minutes. Roughly chop or shred chicken and return to pan. Add cream and boil 8 to 10 minutes, then remove bay leaves and thyme and parsley sprigs. Add green beans, peas, and chopped parsley; season with salt and pepper. Divide mixture into ramekins and top with prepared dough. Poke a few holes through the dough so air can escape. If desired, whisk together egg white and water in a small bowl and brush pastry tops. Place ramekins on a baking sheet and bake about 20 minutes, or until golden brown.