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Question

Try replacing this:

        <?php
            /* Include the Post-Format-specific template for the content.
             * If you want to override this in a child theme, then include a file
             * called content-___.php (where ___ is the Post Format name) and that will be used instead.
             */
            get_template_part( 'content', ( post_type_supports( get_post_type(), 'post-formats' ) ? get_post_format() : get_post_type() ) );
        ?>

With this:

<?php echo my_excerpt(get_the_ID(), 300, 'Read More'); ?>

And then add this to your functions.php file:

function my_excerpt($postid, $len = 500, $more = false) {

    $excerpt = apply_filters('the_excerpt', get_post_field('post_excerpt', $postid));

    if(empty($excerpt)) $excerpt = strip_shortcodes(strip_tags(apply_filters('the_excerpt', get_post_field('post_content', $postid))));

    if(strlen($excerpt) > $len) $excerpt = substr($excerpt, 0, $len-3) . '&hellip;';

    if($more) $excerpt .= '<a class="read-more" href="' . get_the_permalink($postid) . '">' . $more . '</a>';

    return $excerpt;
}

By default that will return the first 300 characters of the post content. Change the “300” in the my_excerpt call to whatever number of characters you want to return (note, this is not how many words to return, but how many characters).