In a 3- to 4-quart stainless-steel saucepan or enameled Dutch oven, combine yogurt, 2 cups (475ml) water, and cornstarch and bring to a boil over medium-high heat, whisking constantly to prevent curdling.
Reduce heat to a bare simmer, whisking occasionally to prevent scorching. Season with salt.
While the yogurt simmers, combine olive oil and garlic in a small skillet and set over medium heat. Cook, stirring and swirling the skillet often, until garlic is fragrant but not browned, 1 to 2 minutes.
Pour the garlic and its oil into the yogurt and stir. The sauce should be quite sour, but will vary based on the yogurt used; add optional lemon juice, if needed.
Stir rice into the yogurt until well combined; season with salt, if needed.
Increase heat slightly and bring to a simmer, then cook, stirring often, until you reach a porridge-like consistency similar to a thin risotto or rice pudding, about 15 minutes.
To serve, ladle the rice into shallow bowls and, if using, top with the toasted nuts and/or dried mint.
