Filling a table asynchronously in Drupal 7

Hello all. I’ve searched around for a solution to this easy problem; all the answers I’ve found seem far too complicated. Here’s what I need:

I have a 2 column table with a list of ~ 15 URLs on the left column. When I click a button, I want all of the URLs to be accessed with the response appearing in the column on the right as they are received from the URL. Each result is only a couple of numbers, or a notice if the source does not respond. The key here is I want the whole operation done asynchronously, not sequentially.

I don’t even know where to start, other than it most likely involves JavaScript and multi-threading on the server. Can someone point me in the right direction? Thanks in advance!

Drupal version: