To make the crust: In the bowl of a food processor, combine the butter, cream cheese, flour and salt. Pulse to combine. Pulse, pulse, pulse until the ingredients start to come together and resembles Parmesan. Add the egg yolk and 1 tablespoon of water. Pulse a couple of more times until the ingredients start to form a ball. If the mixture is exceedingly wet, add some more flour. Or conversely, if the mix is dry, dry, dry, add in a few more drops of water.
When the mixture has come together into a ball, turn it out onto a floured work surface and knead it a couple of times to help it come together. Dust it with flour, form it into a disk and wrap it in plastic wrap. Refrigerate until ready to use. This can be done a day ahead.
Cook's Note: When ready to use the dough, remove it from the refrigerator about 20 minutes before rolling, to allow it to warm up and soften.
To make the filling:
Coat the bottom of a stock pot lightly with olive oil put over medium heat. Add the onions, celery and the carrots and sprinkle with salt, to taste. Saute the vegetables for 7 to 8 minutes. Add the garlic and sweat for another 2 to 3 minutes. Season with salt, then add the chicken and the chicken stock. If the stock doesn't cover the chicken, add water until it does. Bring the stock to a boil, over high heat, then reduce the heat and simmer for 30 minutes.
While the chicken is simmering, add the butternut squash to a large bowl, drizzle with some olive oil and add salt, to taste. Toss to coat the squash with the oil and transfer to a baking sheet. Roast until the squash is cooked but still has some texture, about 15 to 20 minutes. Remove from the oven and reserve.
Remove the chicken and vegetables from the stock and put into a large bowl. Reserve the stock. When the cool enough to handle, remove the bones from the chicken and stir into the vegetables. Add the roasted squash to the chicken and vegetables. Stir to combine and season with salt, if needed. Stir in the haricots verts and the chopped sage.
Melt the butter in a large saucepan over low heat. Add the flour and stir to combine with melted butter. Cook stirring frequently until the mixture is the consistency of wet sand and is starting to turn a little beige, about 6 to 7 minutes. Gradually whisk in the reserved chicken stock. Taste and adjust seasoning, if needed. When the stock is combined into the roux, bring to a boil, then reduce the heat and simmer until it has a gravy-like consistency, about 20 to 25 minutes. If the gravy reduces too much and becomes too thick, whisk in a little more chicken stock or water.
Preheat the oven to 375 degrees F.
Add the chicken mixture into a 2-quart casserole dish or 4 individual (2 cup) crocks. Ladle the "gravy" over the chicken mixture until the dish(s) are 3/4 filled.
Dust a clean work surface with flour and roll the dough into the shape of the casserole dish or large enough to cut circles to cover the individual casserole dishes. Whichever dishes are being used the dough needs to have generous overhang of dough on the edges of the dish. Brush the outside edges of the dish with a little of the egg wash to help "glue" the dough to sides of the dish. Fold the edges of the dough under and press it onto the edges of the dish. Brush the top of the dough with the remaining egg wash. Cut a couple of vents in the top of the dough to allow the steam to escape.
Bake in the preheated oven until the dough is golden brown and the inside is hot and bubbly, about 30 to 35 minutes. Remove from the oven and serve hot.