For the filling: Put chicken, onions, carrots, celery, celery leaves, parsley, sage, pepper, and 12 cups cold water into a large pot. Bring to a boil over high heat, skimming off any foam as it appears. Reduce heat to low and simmer until chicken is very tender, 1 1⁄2–2 hours, depending on weight and age of bird. Transfer chicken with a slotted spoon to a bowl and set aside to let cool briefly. Remove meat from bones and transfer to a bowl; discard skin and return bones to stock. Cover meat with plastic wrap and refrigerate overnight. Increase heat to medium and continue simmering stock until rich and golden, about 3 hours more. Strain stock, discarding solids. Set aside to let cool, then cover and refrigerate overnight.
The next day, remove and discard solid layer of fat from stock, then transfer stock to a medium pot and boil over medium heat until reduced by half (to about 5 cups), 1–1 1⁄2 hours.
Preheat oven to 475°. Cut chicken meat into large pieces and put into a large baking dish in an even layer. Whisk flour and 1 cup water together in a bowl until smooth, then whisk into hot stock in pot over medium heat, whisking constantly, until thickened, 4–6 minutes. Season to taste with salt, then ladle gravy over chicken. Bake until hot and bubbling, 10 minutes.
For the biscuits: Sift flour, baking powder, and salt together into a large bowl. Use 2 table knives to work butter into flour until it resembles coarse meal. Stir in milk with a fork until dough holds together. Transfer to a floured surface and roll dough out to about 1⁄2" thickness. Use a 3" round cookie cutter to cut out 12 disks, rolling dough out again, if necessary.
Remove baking dish from oven and arrange biscuits on top of chicken and gravy in a single layer. Return dish to oven and bake until biscuits are fluffy and golden brown, about 20 minutes. Set pie aside on a rack to let cool for 10 minutes before serving.