In a medium pot, combine the water and rice. Cook over medium heat until the rice is soft and tender.

In a bowl, whisk together the yogurt, flour, egg yolk, and lemon juice until smooth. Slowly add a few spoonfuls of the hot rice water into this mixture while whisking constantly. This helps warm it up gently and prevents the yogurt from curdling.

Slowly pour the warmed yogurt mixture into the pot with the cooked rice. Stir well and cook over low heat, stirring often, until the soup slightly thickens.

Once the soup is done, add the salt and give it a final stir.

Ladle the soup into bowls, drizzle with the reserved butter-mint sauce if you like, and serve warm.