You can do this by using the code below. The code will query the database and will display the total published blog posts count for current logged-in user.
$db = JFactory::getDbo();
$query = $db->getQuery(true);
$query = 'select count(1) as `post_count`';
$query .= ' from `#__easyblog_post` as a';
$query .= ' where a.`created_by` = ' . $user->id;
$query .= ' and a.published = ' . $db->Quote('1');
$postcount = $db->loadResult();
You can use this if you want for example to present to the current logged-in user his total blog posts count. Think about it kinda like a "notification" count. In our case scenario, we built a "My Account" custom menu where we listed some personal menu option for current logged in user. We used the above code to show post count next to "My Blog Posts" menu option.
Enjoy ! I hope you will find a good use !