In a large pot, bring 4 cups of water to a boil. Remove from heat and add tea bags (about 4-6 regular tea bags for strong tea). Steep for 5-7 minutes, then remove tea bags.
Stir in sugar and salt until completely dissolved. Add lemon juice, spent lemon halves, thyme, garlic, and peppercorns.
Allow the mixture to cool to room temperature, then add ice cubes to chill completely.
Place chicken pieces in a large, non-reactive container (glass or food-grade plastic). Pour the cooled sweet tea brine over the chicken, ensuring all pieces are fully submerged.
Cover and refrigerate for 12-24 hours. For best results, turn the pieces halfway through the brining time.
Remove chicken from brine and pat thoroughly dry with paper towels. Allow chicken to sit at room temperature for 30 minutes to take the chill off.
In a large bowl, whisk together buttermilk and eggs. In another bowl, combine flour, cornstarch, and all seasonings. Set up a wire rack over a baking sheet to hold the dredged chicken.
Working with one piece at a time, dip chicken in the buttermilk mixture, allowing excess to drip off. Dredge thoroughly in the flour mixture, pressing gently to ensure coating adheres.
Place on the wire rack and allow to rest for 10 minutes before frying.
Heat oil in a large, heavy-bottomed pot or deep cast-iron skillet to 325°F (use a thermometer for accuracy).
Carefully add chicken pieces in batches, avoiding overcrowding. Fry breast pieces for 12-14 minutes and thighs/drumsticks for 14-16 minutes, turning occasionally, until golden brown and internal temperature reaches 165°F.
Transfer fried chicken to a clean wire rack set over a baking sheet. Allow to rest for 10 minutes before serving.