Scrub potatoes and cut into quarters. Peel carrots, and trim and discard ends; cut carrots diagonally into 1/4-inch-thick slices. Rinse beans, and trim and discard ends; cut beans into 1 1/2-inch lengths.
In a covered 5- to 6-quart pan over high heat, bring potatoes, carrots, broth, and herbs to a boil. Reduce heat and simmer until carrots are almost tender when pierced, about 5 minutes. Add beans; cover and simmer until all the vegetables are tender when pierced, 3 to 5 minutes longer.
In a small bowl, mix cornstarch and cream. Add to vegetable mixture and stir until boiling, about 2 minutes. Remove from heat and stir in chicken. Add salt and pepper to taste. Spoon equally into 6 round soufflé dishes or ramekins (1-cup size; 3 1/2 to 4 1/2 in. wide). Let cool to room temperature, about 35 minutes.
Meanwhile, on a lightly floured board, roll each puff pastry shell into a round about 1 inch wider than the diameter of soufflé dishes. Brush egg around edge of each pastry in a border about 1/2 inch wide. Invert a pastry onto each dish, egg side down, and press edges firmly against sides of dish. Brush egg lightly over pastry tops and sides. Set dishes at least 1 inch apart in a 10- by 15-inch pan.
Bake in a 400° regular or convection oven until pastry is richly browned, 15 to 25 minutes.
One of my families favorite meals. This is the absolute best pot pie ever. You can add or take away some of the seasonings to suit your needs and the same with the veggies. Make it your own, it is fabulous!!!!
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