Thoroughly rinse the chicken, then cover all the pieces with 3/4 cups of buttermilk. Soak in the fridge overnight or up to 24 hours.
When you're ready to fry the chicken, remove the bowl from the fridge and let it sit on the counter for 30 minutes to take off the chill.
Preheat oven to 360°F.
Put the flour, seasoned salt, paprika, pepper, thyme and cayenne (extra cayenne if you like heat) in a very large bowl and stir together well.
In a small bowl, combine the milk and remaining 1/4 cup buttermilk.
Pour into the flour mixture and, with a fork, gradually mix until there are little lumps throughout. This will adhere to the chicken and make for a crispier breading. If necessary, add a little more flour or milk to the bowl in order to make it slightly lumpy.
Heat 1 1/2 to 2 inches of vegetable oil in a deep skillet over medium-high heat until a deep-fry thermometer registers 365°F. Lower the heat slightly, if necessary, to keep the oil from getting hotter.
Thoroughly coat each chicken piece with the breading, pressing extra breading onto the chicken if necessary. Place the breaded pieces on a plate.
Add the chicken to the oil 3 or 4 pieces at a time. Make sure they aren't sticking together, then cover the skillet and fry for 5 to 7 minutes, checking occasionally to make sure the chicken isn't getting too brown.
Turn the pieces over, cover again and cook 3 to 5 minutes more. Monitor the temperature of the oil to make sure the chicken doesn't burn.
Transfer the fried chicken pieces to a baking sheet. They will not be completely cooked through.
Bake the thighs for 15 minutes to finish the cooking process (check with an instant read thermometer for 175°F.) If any pink juice or meat is visible, the chicken needs to continue cooking in the oven.
Cover and keep warm.