Combine buttermilk and 3 tablespoons salt in a large baking dish or a large zip-top bag and mix until salt dissolves.
Submerge the chicken pieces in the buttermilk brine, cover (or seal the bag) and refrigerate for at least 4 hours or overnight.
When ready to cook, whisk together the flour, 1 teaspoon salt, turmeric, paprika, chili powder, and black pepper in a shallow dish or bowl.
Remove each piece of chicken from the brine one at a time, let excess drip off, then dredge in the seasoned flour until lightly coated; place on a prepared baking sheet and repeat with remaining pieces.
Allow dredged chicken to rest on the tray while you heat the oil; this helps the coating adhere.
Fill your broaster, deep fryer, or heavy pot with oil to the manufacturer’s recommended depth (about 2 quarts for a 6–8 qt pot) and heat to 360°F for broaster method or 375°F if using a pot for initial heating.
If using a broaster or deep fryer, carefully lower chicken pieces into the hot oil starting with the breasts, close the lid (if applicable) and cook 8–10 minutes until golden and the internal temperature reads 165°F.
If frying in a Dutch oven, maintain oil between 350–360°F after adding chicken; fry covered for 12–15 minutes until golden and the internal temperature reaches 165°F, checking and adjusting heat as needed.
For Instant Pot sauté (if your model allows 360–375°F), preheat on the 'more' sauté setting, add oil, arrange breasts and remaining pieces, then cover partially if needed and fry 14–16 minutes until the chicken reaches 165°F.
Remove cooked chicken with tongs and transfer to a wire rack to drain and crisp before serving.
