The optimization process and recommendations:

1. 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.
2. Index Function Calls Using Generated Columns (modified query below): When a function is used directly on an indexed column, the database's optimizer won’t be able to use the index to optimize the search. Creating and indexing a generated column (supported in MySQL 5.7) will allow MySQL to optimize the search.

Optimal indexes for this query:

ALTER TABLE `sessions` ADD INDEX `sessions_idx_str_session_date_e` (`str_to_date_concat_date_format_session`,`date_format_session_stop_e`);
ALTER TABLE `sessions` ADD INDEX `sessions_idx_str_session_date_d` (`str_to_date_concat_date_format_session`,`date_format_session_stop_y_m_d`);

The optimized query:

SELECT
        date_format(t.`session_stop`,
        '%d') AS `session_stop`,
        sum(t.`energy_used` / 1000) AS `csum`,
        (SELECT
            (SUM(a.`energy_used`) / 1000) 
        FROM
            `sessions` a 
        WHERE
            a.date_format_session_stop_y_m_d <= a.date_format_session_stop_y_m_d 
            AND t.str_to_date_concat_date_format_session = str_to_date(concat(date_format(now(), '%Y-%m'), '-01'), '%Y-%m-%d') 
        ORDER BY
            str_to_date(date_format(a.`session_stop`,
            '%e'),
            '%d') ASC) AS `sum` 
    FROM
        `sessions` t 
    WHERE
        t.str_to_date_concat_date_format_session = str_to_date(concat(date_format(now(), '%Y-%m'), '-01'), '%Y-%m-%d') 
    GROUP BY
        t.date_format_session_stop_e 
    ORDER BY
        str_to_date(date_format(t.`session_stop`,
        '%d'),
        '%d') ASC