1Preheat oven to 400°F. For the crust:
Place the flour, Parmesan, sugar, and salt in the bowl of a food processor, and pulse a few times to combine. Add the butter and pulse until the butter has been reduced to slightly smaller pieces. With the motor running, slowly add the ice water, until the dough comes together.
2Transfer the dough quickly to a lightly floured surface, and knead it briefly a few times until it forms a ball. Flatten the ball slightly. Wrap the dough in plastic wrap, and refrigerate it while you make the filling.
3For the filling:
In a pot, heat the olive oil over medium-high heat. Add the celery, onions, and carrots, and season with a pinch of salt and pepper. Sauté, stirring occasionally, just until the mixture starts to caramelize.
4Add the potatoes, and sauté until the potatoes start to brown around the edges and the onions are a little more caramelized. Stir in the chicken with another pinch of salt and pepper, and continue to saute, stirring occasionally, until all the meat turns white, about 10 minutes.
5Sprinkle the flour over the chicken and vegetables, stirring well so that the flour evenly coats the mixture, and cook for 1 minute, stirring constantly. Gradually stir in the chicken broth. Bring to a boil over medium heat, stirring constantly. Simmer for a minute.
6Stir in the broccoli and then the peas; heat through. Remove the pot from the heat and stir in the parsley and oregano. Season with more salt and pepper to taste.
7To assemble the potpies:
In a small bowl, whisk together the eggs with a pinch of salt and a little water, and set aside. On a lightly floured surface, roll the dough to a 1/3- inch thickness.
8Cut out 6 rounds that are slightly larger than 6 oven-safe bowls. Ladle the hot filling into the bowls. Top each bowl with a round of dough, fitting the dough inside the bowl rim so that it touches the filling. Flute the edges of the dough.
9Brush the dough with the prepared egg wash.
Cut small slits in the dough to let steam escape. Place the bowls on a baking sheet, and bake until the pastry is golden brown and the filling is bubbly, 30 to 45 minutes. Let stand for 5 minutes before serving.