Hi,
you can create a Easy Profile - Search Module that search only by Format Name*, you can put it everywhere in your template and it allow you to set to show the results in a specific Easy Profile->Users List page.

* Of course this will search only in Joomla name field and not in all searchable fields.

What I mean is like Amazon or Walmart or PsychologyToday where you first use a single search field and then on the results page you can use all of the other search fields to refine your search.

Hi,
yes is possible with "Easy Profile - Search Module", see an example on this site:
in this forum I have just added a module to search by Username in the right column (see screenshot 1), I have set it to redirect at our Users List page where you can perform another search (screenshot 2)

Perfect. How do I get the left-hand block with the search fields (refined search items) on the results page?

I assume a profile menu item with a module with the other fields listed?

I assume a profile menu item with a module with the other fields listed?

Yes, normally Users List menu item allow you to add search form at the top (no need module), instead, like this site, we have used the Search module because it is more flexible.

Can you tell me how I can choose what shows on the results page on the individual profiles such as the screenshot:

In Users List menu item you can choose which fields are visible in the list (see screenshot).
In this site you have different fields for each users for these reasons:

1) Privacy setting, some user have set own informations as Private, so these are not in the list

2) Empty fields, some user have some of displayed fields empty, so these are not in the list

3) Conditions, some fields have a conditions, for example in registration/edit profile pages you can see a field like "Your Job", based on value of this field users have available in own profile different other fields:
- if "Your Job" is equal to "Web Designer" then the user will have on profile a fields called "Know how to use photoshop"
- if "Your Job" is equal to "Developer" then the user will have on profile a fields called "Known languages"
- if "Your Job" is equal to "Other" then the user will have on profile a text fields called "What do you do"

"Know how to use photoshop", "Known languages", "What do you do" are all visible in the list, but for a user who has chosen "Developer" as "Your Job" then it will have available only "Known languages" field

Thank you very much.