Rinse the Rice under cold water until the water runs clear to remove excess starch.
Bring a pot of Water to a boil, season with Salt, add the rinsed rice and cook over medium heat until the rice is tender and the grains have begun to burst, then reduce heat to low and keep some of the cooking liquid hot.
In a mixing bowl, whisk the Plain Full-Fat Yogurt with the Egg Yolk and the All-Purpose Flour until smooth and creamy; add a little cold water if needed to loosen the mixture into a pourable consistency.
Temper the yogurt mixture by slowly whisking in a ladleful of the hot rice cooking liquid to warm it without curdling, then gradually stir the tempered yogurt back into the pot with the rice, mixing thoroughly.
Gently simmer the soup for 3–5 minutes, stirring frequently so it thickens slightly and the flavors meld; adjust seasoning with more Salt if needed.
In a small pan, melt the Unsalted Butter over medium heat until it foams and begins to brown lightly, then add the Dried Mint and let it sizzle for a few seconds to release its aroma.
Pour the minted brown butter over the soup just before serving for a fragrant finish, stir lightly, and serve hot.
