The day before the meal, combine brine ingredients in a large plastic bag. Add chickens and refrigerate for 24 hours.
Preheat oven to 500F.
Boil water in a medium pot and cook onions 3-4 minutes. Drain and cool in ice bath. Squish onions away from their skins, leaving them whole. Place in a shallow roasting dish or casserole. Add potatoes, garlic, lemon slices, olives, bay, rosemary and thyme. Drizzle with EVOO; season with salt and pepper.
Place a cooling rack over baking dish.
Remove chicken from brine and pat dry. Coat skin with EVOO and season with pepper. Arrange chicken over the top of the potatoes and place in oven. Roast 35 minutes at 500F then lower heat to 300F and roast about 20-30 minutes more, until the internal temperature reaches 165F.
Turn off oven and let chickens rest 10 minutes. Remove and serve half chickens with a lemon quarter to squeeze over top and the potatoes, garlic and olives alongside.