Preheat the oven to 400°F. Line a baking sheet with aluminum foil and set aside.

Dust a clean, dry work surface with flour and place the puff pastry on top. Roll the pastry dough making sure to smooth the creases. With a sharp knife, cut out 4 circles about 2 inches larger than the circumference of your bowls. Place the dough aside until ready to use.

To make the filling, heat a large sauté pan over medium-high heat, and melt the butter. Add in the onions, carrots, and green beans. Sauté for 8 to 10 minutes, or until the carrots are just cooked. Add in the flour and cook, stirring constantly, for about 2 minutes.

Pour in the broth and bring to a boil. Stir and simmer until thickened. Reduce the heat to low and stir in the chicken and the heavy cream. Season with thyme, and salt/pepper to taste.

Ladle the pot pie filling into oven-safe soup bowls and place the pastry dough rounds over the soup bowls. Press firmly around the edges so that the dough adheres, and then brush the top of the dough with the egg wash. (To make egg wash, beat 1 egg with 1 tablespoon of water). Make a small slit in the top of each pie and transfer the bowls to the foil-lined baking sheet. Bake for 20 to 25 minutes, or until the pastry is a rich golden brown.

Let cool for about 10 minutes, before transferring the hot bowls to serving plates. Sprinkle with a little fresh thyme, if desired, and serve.