Chicken pie makes me think of rainy days, sweaters and curling up with my mom on the couch to watch "Jeopardy." This is such a homey, simple dish. What I love about it is that you can add whatever leftovers you like: peas, carrots, kale, sausage, cheese, odds and ends of all kinds. This isn't a super rich chicken pot pie, where the sauce inside the pie is a thick bechamel. This pie strikes a nice balance and the buttermilk biscuit crust adds the perfect tang to every bite.
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.
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.
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.
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.)
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.
Bake until the crust is a deep golden brown, 30 to 40 minutes.
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.
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.)
Divide the dough into 2 rectangles and wrap each in plastic wrap or parchment and refrigerate for 30 minutes.
The key to fluffy, light biscuits is ice-cold ingredients, so make sure your butter and buttermilk are thoroughly chilled, and that you're working lightly and quickly. If you need to pause the process, pop the ingredients in the fridge to keep them cold.