json_grouping.php

<?php

$in = <<<'JSON'
[
    {
        "Date": "2014-12-01",
        "StartTime": "10:00",
        "EndTime": "16:00"
    },
    {
        "Date": "2014-12-02",
        "StartTime": "12:00",
        "EndTime": "18:00"
    },
    {
        "Date": "2014-12-03",
        "StartTime": "10:00",
        "EndTime": "20:00"
    },
    {
        "Date": "2014-12-03",
        "StartTime": "12:00",
        "EndTime": "20:00"
    }
]
JSON;

$data = json_decode($in, true);
$out = [];

foreach($data as $element) {
        $out[$element['Date']][] = ['StartTime' => $element['StartTime'], 'EndTime' => $element['EndTime']];
}

var_dump(json_encode($out, JSON_PRETTY_PRINT));