Grouping data while looping by one value and push another value into the group as a subarray value

I currently have this code:

$files = glob('songs/*.{mp3}', GLOB_BRACE);
$dateUploaded = array();

foreach ($files as $file) {
    $path_parts = pathinfo($file);
    $dateUploaded[] = array("Date Uploaded" => date ("jS \of F,  Y", filemtime($file)), "File Name" => $path_parts['filename']);
}
print_r($dateUploaded);

Which outputs

Array (
    [0] => Array (
        [Date Uploaded] => 26th of February, 2013
        [File Name] => All That Glitters - This Sound (Felix Cartal Remix)
    )
    [1] => Array (
        [Date Uploaded] => 26th of February, 2013
        [File Name] => Bertie Blackman - Hide and Seek
    )
    [2] => Array (
        [Date Uploaded] => 18th of December, 2012
        [File Name] => Birds of Tokyo - This Fire
    )
    [3] => Array (
        [Date Uploaded] => 18th of December, 2012
        [File Name] => Bloc Party - Truth
    )
    [4] => Array (
        [Date Uploaded] => 18th of December, 2012
        [File Name] => C2C - Down the Road
    )
    [5] => Array (
        [Date Uploaded] => 18th of December, 2012
        [File Name] => Chance Waters - Young and Dumb feat Bertie Blackman
    )
    [6] => Array (
        [Date Uploaded] => 26th of February, 2013
        [File Name] => City Calm Down - Sense of Self
    )
    [7] => Array (
        [Date Uploaded] => 18th of December, 2012
        [File Name] => Clubfeet - Heartbreak
    )
    [8] => Array (
        [Date Uploaded] => 26th of February, 2013
        [File Name] => Cosmo Jarvis - My Own Thing
    )
    [9] => Array (
        [Date Uploaded] => 6th of June, 2013
        [File Name] => Courtney Barnett - History Eraser
    )
    [10] => Array (
        [Date Uploaded] => 6th of June, 2013
        [File Name] => Delphic - Baiya
    )
)

What I am trying to do it group these by the "Date Uploaded" key. So I have something that resembles this:

Array (
    [26th of February, 2013] => Array (
        [0] All That Glitters - This Sound (Felix Cartal Remix)
        [1] Bertie Blackman - Hide and Seek
        [2] City Calm Down - Sense of Self
        [3] Cosmo Jarvis - My Own Thing
    )
    [18th of December, 2012] => Array (
        [0] Birds of Tokyo - This Fire
        [1] Bloc Party - Truth
        [2] C2C - Down the Road
        [3] Chance Waters - Young and Dumb feat Bertie Blackman
        [4] Clubfeet - Heartbreak
    )
    [6th of June, 2013] => Array (
        [0] Courtney Barnett - History Eraser
        [1] Delphic - Baiya
    )
)

The main goal that I am trying to achieve is to be able to just put files in a folder on my server and have my script print out, in the form up a <ul>, the songs grouped by date uploaded.

i.e.

<ul>
    Last Updated: 26th of February, 2013
    <li>All That Glitters - This Sound (Felix Cartal Remix)</li>
    <li>Bertie Blackman - Hide and Seek</li>
    <li>City Calm Down - Sense of Self</li>
    <li>Cosmo Jarvis - My Own Thing</li>
</ul>
<ul>
    Last Updated: 18th of December, 2012
    <li>Birds of Tokyo - This Fire</li>
    <li>Bloc Party - Truth</li>
    <li>C2C - Down the Road</li>
    <li>Chance Waters - Young and Dumb feat Bertie Blackman</li>
    <li>Clubfeet - Heartbreak</li>
</ul>
<ul>
    Last Updated: 6th of June, 2013
    <li>Courtney Barnett - History Eraser</li>
    <li>Delphic - Baiya</li>
</ul>

foreach($files as $file){
    $path_parts = pathinfo($file);
    $date = date ("jS \of F,  Y", filemtime($file));
    if(isset($dateUploaded[$date])) {
          $dateUploaded[$date][] = $path_parts['filename'];
    } else {
          $dateUploaded[$date] = array($path_parts['filename']);
    }
}