5 teaspoons coarse kosher salt plus additional for serving
6 cups buttermilk
12 cups peanut oil (for deep-frying)
Fresh rosemary and thyme sprigs (for garnish), deep-fried 30 seconds
Bring all brine ingredients except chickens to boil in large pot. Boil 1 minute, stirring to dissolve salt. Cool completely. Chill brine until cold, about 2 hours.
Rinse chickens; add to brine, pressing to submerge. Chill at least 12 hours and up to 24 hours. Drain chickens and pat dry, removing any herbs or spices sticking to the skin. Cut each chicken into 8 pieces.
Line 2 large baking sheets with parchment paper. Mix first 6 ingredients and 4 teaspoons coarse salt in large bowl. Place buttermilk in another large bowl. Dip each chicken piece in flour mixture to coat; shake off excess. Dip pieces in buttermilk, coating completely, then dip into flour mixture again, coating thickly (do not shake off excess). Place chicken on prepared sheets. Let stand 1 to 2 hours at room temperature to dry.
Pour peanut oil into heavy large pot. Attach deep-fry thermometer to side of pot and heat oil over medium-high heat to 320 degrees Fahrenheit and 330 degrees Fahrenheit. Working in batches of 4 pieces at a time, add leg and thigh pieces to oil (use splatter screen to protect yourself from hot oil). Adjust heat as needed to maintain temperature. Fry until cooked through and skin is deep golden brown, turning once with wooden spoons (to prevent crust from breaking), about 13 minutes. Using wooden spoons, transfer chicken to paper towels to drain. Sprinkle with course salt.
Add breast pieces to oil and fry until cooked through and skin is deep golden brown, turning once, about 7 minutes. Transfer chicken to paper towels to drain. Sprinkle with course salt.