Aguadita (Peruvian Chicken Soup)

Ingredients

• very hot red pepper hot sauce (to taste for garnish)
• 3 limes, quartered
• 4 scallions, thinly sliced
• 6 hard-boiled eggs, peeled and halved
• 1 bunch cilantro leaves, minced (plus more whole leaves for garnish)
• salt
• pepper
• 1 5 lb. stewing chicken or hen
• 2 leeks, trimmed, roughly chopped, and washed well
• 2 stalks celery, roughly chopped
• 2 carrots, roughly chopped
• 1 ear corn (or hominy) cut into 6 like sized rounds
• 1 one inch piece ginger, peeled and smashed
• 1 cup rice
• 6 medium yukon gold potatoes, peeled and halved
• 1 head garlic, halved crosswise