Chicken Pie

1. Preheat the oven to 425 degrees F.
2. In a large pot, combine the chicken, onion and 2 cups water. Cover, and bring to a simmer, then let simmer until the meat pulls away from the bones easily, about 30 minutes.
3. Transfer the chicken to a cutting board. Transfer the onions with a slotted spoon to a large bowl. Slice or pull the meat off the chicken bones, keeping it in large pieces and transfer it to the bowl; discard the bones. Season with salt and pepper. Toss with the 2 tablespoons flour and set aside. Reserve the cooking liquid.
4. Whisk together the eggs, herbs and the 1 1/2 cups half-and-half in another large bowl. Add the chicken filling, and enough of the reserved cooking liquid to just cover the chicken. Set aside.
5. Roll 1 rectangle of the biscuit dough on a lightly floured counter to about 1/4 inch thick. Line a 10-inch deep-dish pie pan with the dough. Add the chicken mixture, filling the pan about 3/4 full. (Don't overload the pie with the filling or it will bubble out of the vents.)
6. Roll out the second rectangle of biscuit dough about 1/4 inch thick and drape it over the pie. Cut vents on top and crimp the edges of the 2 crusts together with your fingers. Brush the top crust with half-and-half.
7. Bake until the crust is a deep golden brown, 30 to 40 minutes.

Biscuit Dough:

1. Scatter the butter over the 4 1/2 cups flour in a large bowl. Cut the butter into the flour with a pastry cutter (or with your fingertips) until crumbly and the mixture resembles small peas. Add the 2 cups buttermilk, stirring just until the dry ingredients are moistened, and the dough comes together in a ball.
2. Turn the dough out onto a lightly floured surface; knead 3 or 4 times to form it into a ball. With floured hands, pat the dough into a 3/4-inch-thick rectangle and fold in thirds like a letter. Pat the dough again to 3/4 inch thick, and repeat this entire process 2 more times. (This creates the fluffy layers that will puff and add lift as the biscuits bake.)
3. Divide the dough into 2 rectangles and wrap each in plastic wrap or parchment and refrigerate for 30 minutes.