Another poossible solution is based on the array_search() function. You need to use PHP 5.5.0 or higher.

Example

$userdb=Array
(
    0 => Array
        (
            "uid" => '100',
            "name" => 'Sandra Shush',
            "url" => 'urlof100'
        ),

    1 => Array
        (
            "uid" => '5465',
            "name" => 'Stefanie Mcmohn',
            "pic_square" => 'urlof100'
        ),

    2 => Array
        (
            "uid" => '40489',
            "name" => 'Michael',
            "pic_square" => 'urlof40489'
        )
);

$key = array_search(40489, array_column($userdb, 'uid'));

echo ("The key is: ".$key);
//This will output- The key is: 2

Explanation

Summary

array_search('breville-one-touch-tea-maker-BTM800XL', array_column($products, 'slug'));

or, if you prefer:

// define function
function array_search_multidim($array, $column, $key){
    return (array_search($key, array_column($array, $column)));
}

// use it
array_search_multidim($products, 'slug', 'breville-one-touch-tea-maker-BTM800XL');

The original example(by xfoxawy) can be found on the DOCS.
The array_column() page.

Update

Due to Vael comment I was curious, so I made a simple test to meassure the performance of the method that uses array_search and the method proposed on the accepted answer.

I created an array which contained 1000 arrays, the structure was like this (all data was randomized):

[
      {
            "_id": "57fe684fb22a07039b3f196c",
            "index": 0,
            "guid": "98dd3515-3f1e-4b89-8bb9-103b0d67e613",
            "isActive": true,
            "balance": "$2,372.04",
            "picture": "http://placehold.it/32x32",
            "age": 21,
            "eyeColor": "blue",
            "name": "Green",
            "company": "MIXERS"
      },...
]

I ran the search test 100 times searching for different values for the name field, and then I calculated the mean time in milliseconds. Here you can see an example.

Results were that the method proposed on this answer needed about 2E-7 to find the value, while the accepted answer method needed about 8E-7.

Like I said before both times are pretty aceptable for an application using an array with this size. If the size grows a lot, let's say 1M elements, then this little difference will be increased too.

Update II

I've added a test for the method based in array_walk_recursive which was mentionend on some of the answers here. The result got is the correct one. And if we focus on the performance, its a bit worse than the others examined on the test. In the test, you can see that is about 10 times slower than the method based on array_search. Again, this isn't a very relevant difference for the most of the applications.

Update III

Thanks to @mickmackusa for spotting several limitations on this method:

• This method will fail on associative keys.
• This method will only work on indexed subarrays (starting from 0 and have consecutively ascending keys).

Note on Update III

• not taking performance into account: you can use array_combine with array_keys & array_column to overcome this limitation in a one-liner like:

$product_search_index = 
array_search( 'breville-one-touch-tea-maker-BTM800XL', array_filter( array_combine( array_keys($products), array_column( $products, 'slug' ) ) ) );