The optimization process and recommendations:

1. Avoid Subqueries (query line: 13): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
3. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.

Optimal indexes for this query:

ALTER TABLE `fav_food` ADD INDEX `fav_food_idx_user_id` (`user_id`);
ALTER TABLE `food` ADD INDEX `food_idx_f_id` (`f_id`);
ALTER TABLE `food_image` ADD INDEX `food_image_idx_rank` (`rank`);
ALTER TABLE `food_image` ADD INDEX `food_image_idx_f_id_rank` (`f_id`,`rank`);

The optimized query:

SELECT
        food.f_id,
        food.description,
        img.minimgrank,
        i.img_url AS profile_photo 
    FROM
        fav_food 
    INNER JOIN
        food 
            ON fav_food.f_id = food.f_id 
    LEFT OUTER JOIN
        (
            SELECT
                food_image.f_id,
                Min(food_image.rank) AS minImgRank 
            FROM
                food_image 
            GROUP BY
                food_image.f_id 
            ORDER BY
                NULL
        ) img 
            ON img.f_id = food.f_id 
    JOIN
        food_image i 
            ON i.rank = img.minimgrank 
    WHERE
        fav_food.user_id = ?