Place the chicken thighs into a shallow baking dish or gallon-sized zip-top bag.
Pour in the pickle brine and turn chicken to coat.
Marinate, turning, from time to time, for at least an hour, up to about eight hours.
Pour the buttermilk into a wide, shallow bowl.
Into another wide, shallow bowl, place the flour, cornstarch, onion powder, garlic powder, paprika, cayenne, salt, and pepper. Whisk together well.
Set a 12-inch cast iron skillet or 5-quart Dutch oven over medium-high heat and pour in safflower oil to a depth of two inches. Heat to 350°F. (You'll cook the chicken at 325°F — starting the oil at a higher temperature accounts for the drop that will occur when you add the chicken.)
Dip each thigh into the buttermilk and dredge to coat well, then allow any excess to drip off. Then dredge through the flour mixture, turning and patting as necessary to achieve a thick, even coating. If you like, you can repeat this process to create a double layer of extra-thick breading.
When you've coated all four thighs, add them to the hot oil. Cook, turning every minute or two and adjusting heat as necessary to maintain the oil temperature at 325°F, until golden brown and cooked through to 165°F.
Drain on paper towels and sprinkle with salt. I find that the chicken stays hot for quite a while, but if you're making multiple batches, you can place the cooked pieces on a metal rack set over a rimmed sheet pan and keep them warm in a 250°F oven.