Step 1
Place a rack in center of oven; preheat to 425°. Pulse 1 tsp. baking powder, ½ tsp. baking soda, 2 cups all-purpose flour, and 1½ tsp. Diamond Crystal or 1 tsp. Morton kosher salt in a meals processor. Add ½ cup (1 stick) chilled butter, minimize into small items; pulse till crumbly and largest items of butter are pea-size. Switch to a bowl and fold in 1 cup bitter cream.
Step 2
Prove dough onto a floor; pat right into a rectangle. Fold in half, pat out once more. Repeat 1 extra time, then kind into an 8×4″ rectangle; minimize into 4 items. Switch to a parchment-lined baking sheet.
Step 3
Combine remaining 1 Tbsp. bitter cream and a drizzle of water in a small bowl (it ought to be the consistency of heavy cream); brush tops of biscuits with bitter cream combination. Sprinkle with a little bit salt. Bake, rotating baking sheet as soon as, till golden brown, 18–22 minutes.
Step 4
In the meantime, warmth 2 tsp. vegetable oil in a big skillet over medium-high. Add 1 lb. floor rooster, 2 tsp. Cajun seasoning, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt and prepare dinner, breaking apart meat into small items with a wood spoon, till browned and cooked by means of, about 5 minutes. Switch rooster to a plate.
Step 5
Soften remaining 3 Tbsp. unsalted butter, minimize into small items, in similar pan over medium-high warmth. Add 1 small onion, finely chopped, 1 small pink bell pepper, finely chopped, 2 celery stalks, finely chopped, remaining 1 Tbsp. Cajun seasoning, and 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt and blend to mix; season with freshly floor black pepper. Cook dinner, stirring often, till greens are softened and calmly browned, 8–10 minutes.
Step 6
Sprinkle in remaining 3 Tbsp. all-purpose flour and prepare dinner, stirring to coat, till golden, about 2 minutes. Scale back warmth to medium-low. Stirring always, steadily pour in 2½ cups entire milk, stopping often to mix and let thicken earlier than including extra, about 4 minutes complete. (Gravy ought to be barely runnier than you count on; it can thicken if you add the rooster and because it cools.)
Step 7
Stir 1 tsp. apple cider vinegar, ½ tsp. crushed pink pepper flakes, and reserved rooster into gravy; style and season with salt and black pepper. Divide gravy amongst plates and high with coarsely chopped parsley. Serve with biscuits.