You can display it in a module exactly how it displays on profile using CB Content Module and substituting it in. Please see the below tutorial for substitution usage information.
www.joomlapolis.com/support/tutorials/107-use-cases/18353-using-substitutions-throughout-cb
Please note you need the "Original Field Value" substitution for it to display with HTML. You'll also need to ensure under CB Content Module advanced parameters that it's configured to load in CBs template CSS. Now you need to be sure the substitution is surrounded by CBs template class. So for example you'd use the below.
Code:
<div class="cb_template">
[cb:userfield field="FIELD_NAME" /]
</div>
Note the above CSS class can probably also just be done with module class suffix parameter, but I haven't tested it.