Dice the celery and chop the chicken. Spray a 2 1/2 or 3-quart casserole dish with cooking spray. Preheat your oven to 400 degrees.
For filling: Melt butter in a large skillet over medium-low heat. Add celery and saute till crisp tender.
Whisk in the flour till it is all absorbed. Then whisk in the broth and milk. Turn heat to medium and continue cooking and stirring till mixture comes to a boil. Boil and stir for at least a minute.
Add seasonings, chicken, and vegetables, stir until combined. Turn the heat to the very lowest setting while you prepare the biscuits.
For biscuits: Whisk together the flour, baking powder, baking soda, sugar, and salt in a mixing bowl. Pour buttermilk into a 1 cup liquid measuring cup. Stir in the melted butter. It will harden into little butter chunks-that's what you want.
Pour the liquid over the dry ingredients and stir lightly. Pat out onto a floured surface until about 1/2" thick. Cut into circles with a biscuit cutter.
Pour the hot filling into the prepared dish. Arrange the biscuits over the top. Feel free to use scraps of dough to fill in the holes.
Bake at 400° for about 30 minutes, or until filling is bubbly and biscuits are golden brown.
Notes
My family likes a thick and hearty filling. If you want yours more saucy, add an additional 1/2 cup of milk or chicken broth.