Pour the buttermilk into a large baking dish or zip-top bag, stir in 3 tablespoons salt, then add the chicken pieces making sure they are fully submerged. Cover or seal and refrigerate for at least 4 hours or overnight.
In a shallow dish or bowl combine the flour, 1 teaspoon salt, turmeric, paprika, chili powder, and black pepper; mix thoroughly.
Set a baking sheet or tray nearby. Remove one piece of chicken at a time from the buttermilk, let excess drip off, then dredge in the seasoned flour, tapping gently to remove excess. Arrange coated pieces on the sheet and dredge all pieces before heating the oil to allow the coating to rest.
Prepare your frying vessel: if using a broaster follow manufacturer instructions and preheat oil to 360°F. If using a Dutch oven or deep pot, fit a thermometer and heat oil to 375°F.
If deep-frying in a pot, carefully add chicken pieces to the hot oil a few at a time (start with breasts), monitoring temperature and keeping it between 350–360°F; gently move pieces so they fry evenly.
Cover with a lid (if using a broaster or as directed) and fry until golden and an instant-read thermometer inserted into the thickest part reads 165°F—about 8–10 minutes in a broaster or 12–15 minutes in a Dutch oven; adjust times for Instant Pot sauté method per manufacturer guidance (about 14–16 minutes with lid partially covering if required).
When cooked, remove chicken with tongs and transfer to a wire rack to drain and rest briefly before serving.