What you have there in your {jrCore_list call is a request to get some stuff. in your call there is no template="some_template.tpl" parameter, so by leaving that out you are saying "Just format it in the default way".
If you want to format it differently, use the template="" parameter. Then in that template you can format it any way you like.
The normal way would be to copy the code from the module and use that as the template.
Eg for your code above you have
{jrCore_list module="jrProfile" order_by="_item_id desc" search1="profile_active = 1" pagebreak="36" page=$_post.p pager=true}
To use the jrProfile's item_list.tpl in there, but tweak it a bit, you can either put that in a template file in your skin and give it a name, or you can use the smarty 'capture' feature to avoid needing to have another .tpl file in your skin. Either works.
Using a capture, it would look like this:
{capture name="row_template" assign="template"}
{literal}
{if isset($_items)}
{foreach from=$_items item="item"}
<div class="item">
<div class="container">
<div class="row">
<div class="col2">
<div class="block_image">
<a href="{$jamroom_url}/{$item.profile_url}">{jrCore_module_function function="jrImage_display" module="jrProfile" type="profile_image" item_id=$item._profile_id size="large" crop="auto" class="iloutline img_scale" alt=$item.profile_name title=$item.profile_name width=false height=false}</a>
</div>
</div>
<div class="col10 last">
<div class="p10">
<h1><a href="{$jamroom_url}/{$item.profile_url}">{$item.profile_name}</a></h1>
{if !empty($item.profile_bio)}
<br><span class="normal">{$item.profile_bio|jrCore_format_string:$item.profile_quota_id|truncate:250:"..."}</span>
{/if}
</div>
</div>
</div>
</div>
</div>
{/foreach}
{/if}
{/literal}
{/capture}
{jrCore_list module="jrProfile" order_by="_item_id desc" search1="profile_active = 1" pagebreak="36" page=$_post.p pager=true template=$template}
That part in the capture was taken from the latest version of:
/modules/jrProfile/templates/item_list.tpl
Adjust it however you like to only alter how that particular jrCore_list is formatted.