I decided to forgo the traditional chicken pot pie — you know the one full of chicken, peas, carrots, and celery. I wanted this one to be a little French.
The saucy sauce that brought the dish together was made with a little olive oil, butter, flour, chicken stock, and an abundance of fresh tarragon — the French part of the dish. Don’t all French recipes seem to use so much tarragon? The tarragon seemed to make what can otherwise be a heavy meal light. The pot pie was fresh-tasting, and the vegetables were still slightly crisp, not overcooked.
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Preheat the oven to 400 degrees.
Butter 2 large ramekins or 4 smaller ones. Heat 1 tablespoon of the olive oil in a large Dutch oven over medium heat. Add the shallot, stir, and cook until softened, about 3 minutes. Add the carrot and celery, stir, and cook for 5 more minutes.
Add the green beans, yellow squash, and russet potato. Stir and cook for 5 minutes. Add the garlic and tarragon, stir, and cook for 1 minute. Remove from the heat and set aside.
In a small saucepan, heat the butter and remaining olive oil over medium heat until the butter is melted. Whisk in the flour, and continue cooking until slightly bubbly, about 1 minute. Add the chicken broth, whisk until smooth, and cook over low heat until thickened, about 3-5 minutes. Season with salt and pepper, to taste.
Pour the sauce over the vegetable mixture, and gently stir in the chicken. Pour the mixture into the ramekins. Cut the puff pastry into pieces slightly larger than the tops of the ramekins. Cover the tops of the ramekins with the puff pastry. Lightly crimp the sides of the puff pastry over the sides.
In a bowl, beat the egg with the water, and gently brush the tops of the puff pastry with the egg wash. Put the ramekins onto a baking sheet and slide into the oven. Bake until the tops are golden and the insides are bubbly (the filling will begin to come out the sides), about 25-35 minutes.