Heat the olive oil in a large pot over medium heat. Add the onion and cook until softened, about 5 minutes.
Whisk in the flour and cook for 1-2 minutes, stirring constantly.
Gradually whisk in the chicken broth, making sure there are no lumps.
Bring to a simmer and cook for 15-20 minutes, stirring occasionally.
Remove from heat and let cool slightly.
In a separate bowl, whisk the yogurt with a few tablespoons of the warm broth to temper it. This prevents curdling.
Slowly whisk the tempered yogurt into the soup. Do not boil after adding the yogurt.
If desired, stir in the cooked rice to thicken the soup.
Season with salt and pepper to taste.
Serve hot, garnished with fresh mint.