1. Prepare Basic Brine, increasing water to 8 cups, thyme and sugar to 2 tablespoons each, and halved lemons to 2.
2. Split shrimp shells down the back, and devein shrimp, leaving shells intact. Place shrimp in a large bowl; add brine. Cover bowl; refrigerate 1 hour.
3. Immerse and soak the cedar planks in water for 1 hour; drain.
4. Preheat a charcoal fire to high heat. Let burn 30 minutes or until flames subside and coals are glowing. Spread coals to an even 4-inch thickness; fan excess ash from coals with a piece of cardboard.
5. Drain shrimp; discard brine. Pat shrimp dry with paper towels. Combine oil and next 8 ingredients (through red pepper) in a large bowl, stirring with a whisk. Add shrimp; toss to coat. Arrange shrimp in 2 tight rows on each plank, with shrimp curled against each other.
6. Place plank on the coal bed with some coals on the exposed corners of the plank. Cover with grill lid; grill 6 minutes or until shrimp are done. Place shrimp on a platter; top with chives and juice.