In a large Dutch oven or heavy-bottomed pot over medium heat, melt butter. Add the potato, carrots, celery, and onion. Add the celery seed and thyme after seasoning with salt and pepper. Sauté for 25 to 30 minutes, or until the vegetables are soft and the onions are transparent. Occasionally stir to prevent browning of the veggies. In order to burn off the alcohol, add the white wine and heat for about one minute.

Add the flour, peas, and chicken and stir. Cook, stirring constantly, for about 3 minutes or until the flour flavor is completely cooked.

Add the chicken stock and stir. Stirring frequently, bring the mixture to a boil and simmer for three to five minutes, or until it thickens. Add the cream cheese and stir until melted. After turning off the heat, give the filling ten minutes or so to cool.

Roll out the dough by placing half of it on a flour-dusted tabletop and dusting it with flour. To soften the dough, dust the rolling pin with flour and roll it six or eight times over the dough. Turn the dough over, give it a quick dusting of flour, and rap it once more, but in the other direction.

Roll the dough away from you, starting in the middle and giving it a quarter turn every couple of passes. Turn the dough over and roll it out again, rolling from the center out. Each time, give the dough a quarter turn and dust the roller and flour as necessary.

Roll out the dough to a thickness of ¼ inch and make it a few inches bigger than the glass pie pan (9 inches). Gently fold the dough in half, then lift it from the rolling surface into the pan in one motion. The dough circle should be unfolded and carefully eased into the pan. The dough will shrink and bounce back as it heated up in the oven if you press it down too much into the pan.

Set oven temperature to 400°F.

Pour the slightly chilled chicken filling mixture into the pie pan, adjusting the filling level if necessary in the center. Place the remaining pie dough disk, which you have rolled out, on top of the pie. Making a large edge, fold the top and bottom layers of pie dough beneath one another on the pie pan's lip. Repeat along the crust's edges, crimping the edge with a fork's tines or fluteing it by pressing your knuckle between the middle finger and index finger of your opposing hand.

Brush the top of the pie crust with one egg that has been whisked with a little milk or half and half. Add a small pinch of kosher salt and a few freshly ground black pepper (optional). Make three to five incisions on the pie's top. Pie should be baked for 45 to 50 minutes, or until bubbling and golden brown, on a sheet pan. To let the filling to solidify, cool for ten to thirty minutes before serving.