Preheat the broiler. Arrange the bread in a single layer on a baking sheet; brush with olive oil and broil, turning once, until golden, 3 to 4 minutes. Rub the toasts with the cut side of the halved garlic.
In a dutch oven, heat 2 tablespoons olive oil over medium-high heat. Season the chicken with salt and pepper. Working in batches, add to the pot and cook, turning once, until golden, about 5 minutes; transfer to a plate.
Add the sliced garlic to the pot and cook, scraping up the browned bits, until lightly golden, 10 to 15 seconds. Add the chicken broth, 2 cups water and the chicken and bring to a simmer; transfer the chicken back to the plate. Add the couscous and lemon peel to the pot, lower the heat to medium-low and simmer for 5 minutes. Shred the chicken into bite-size pieces and return to the soup along with any juices.
In a small bowl, whisk together the eggs and lemon juice. Slowly whisk about 1 cup of the hot soup into the egg mixture, then stir the egg mixture into the soup (the soup will thicken immediately). Remove from the heat and stir in the parsley.