In a large bowl or pot, dissolve 1/2 cup kosher salt in 3 quarts of water. Rinse chicken pieces and add to bowl. Cover and refrigerate for 2 hours. Remove chicken pieces and rinse under cool water. Clear space in the refrigerator to accommodate a wire cooling rack.
Mix together the next 5 ingredients (flour through pepper) and place in a large sealable plastic storage bag. Shake. In a medium bowl, whisk the eggs and then whisk in the buttermilk. Dip 1/2 the chicken pieces in the buttermilk, then place in the plastic bag. Shake, and place on a wire rack. Repeat for remaining pieces. Put the rack on a baking sheet and place in the refrigerator for at least 1 hour, but preferably 2 hours.
Put peanut oil in a large iron Dutch oven to a depth of 3/4-inch. Place over medium-high heat.
When oil reaches 365 degrees F (if you don't have a thermometer, simply wait until the oil starts to smoke, arrange chicken pieces in the pan, skin side down, and cover pan. After 5 minutes remove the cover. Adjust heat level if necessary so that oil bubbles at a moderate pace; not too rapidly and not too slowly. Rearrange pieces if some are browning more quickly than others. After 5 more minutes, turn the pieces over. Cook uncovered for 8 to 10 more minutes or until done. Meanwhile, thoroughly wash and dry the wire rack while the chicken is cooking.
Remove the fried chicken to the cleaned wire rack set over a baking sheet. Let drain for 5 minutes and serve.
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