Wash, scrub, and dry the zucchini. Cut off the stem tips and gently hollow out the centers using a vegetable corer. Treat this step just like carving a pumpkin, leaving a ¼ to ⅓-inch (about ¾ cm) wall around the interior.
Place the rice in a colander, rinse it under cold running water, and gently rub it with your hands to remove as much excess starch as possible. Drain well."
In a bowl, mix the rice with the ground meat and oil, then season with the spices and salt. Your filling is now ready.
Using your fingers, stuff each zucchini with the rice and meat filling, leaving about ¼ inch (½ cm) of space at the top to allow the rice to expand as it cooks. It is important not to overstuff them. Secure the opening of each zucchini with a piece of the reserved zucchini flesh to create a barrier and prevent the filling from leaking out.
Transfer the stuffed zucchini to a large pot and gently add enough water to almost cover them. Sprinkle with about 1 tablespoon of salt and bring to a boil. Reduce the heat to low, cover, and simmer for about 20 minutes until cooked. Drain the zucchini and reserve the broth.
Sprinkle with about 1 tablespoon of salt and bring to a boil. Reduce the heat to low, cover, and simmer for about 20 minutes, or until the zucchini are tender. Drain the zucchini and reserve the cooking broth for the yogurt sauce.
In a large pot, combine the yogurt, garlic, 3 cups of the reserved zucchini broth, and the diluted cornstarch. Whisk well until smooth. Place over high heat and continue whisking constantly in one direction. Pay close attention to the yogurt to prevent it from curdling; continuous whisking is crucial.
Once the mixture comes to a boil, gently add the drained zucchini one at a time. Stir in the dried mint and adjust the salt to taste. Reduce the heat to low and simmer uncovered for 1 hour, allowing the zucchini to cook through and the flavors to meld.
Transfer to a large serving bowl or individual shallow bowls. Serve warm or at room temperature. Refrigerate any leftovers promptly in an airtight container. Bon appétit!