How to Make It
Bring the water to a boil in a medium saucepan. Add the rice, cover and cook over low heat until barely tender, about 15 minutes.
Meanwhile, in a medium saucepan, bring the stock to a simmer over moderately high heat. Add the chicken and simmer until cooked through, about 10 minutes. Using a slotted spoon, transfer the chicken to a plate. Skim any fat from the surface of the stock.
In a large saucepan, whisk the yogurt with the egg yolk and flour. Whisk in the stock and bring to a simmer over low heat, whisking occasionally. Stir in the chickpeas, rice and reserved chicken. Season with salt and pepper and keep warm over low heat.
Melt the butter in a small skillet. Add the garlic, paprika and cayenne and cook over moderate heat until fragrant, about 2 minutes. Ladle the soup into bowls and swirl in the garlic butter. Sprinkle with the mint and serve with lemon wedges.