Laravel: reading available months and years from timestamp to populate a <SELECT>

Question

I have a films table which a timestamps column CREATED_AT. THe format is:

name            created_at
Pocahontas      2016-12-28 22:09:24

I know how to select films from the table added this current month

    $year_month_film = DB::table('films')
        ->select('films.*')
        ->whereMonth('films.created_at', '=', Carbon::now()->month)
        ->orderBy('films.created_at', 'desc')
        ->get();

But now I want to let the user to select dynamically a list of films added on any month of any year (see the image):

I built two in the HTML view in order to select dynamically the films added any month of any year.

<div class="pull-right">
            <select>
              <option value="all" selected>Months</option>
              <option value="January">January</option>
              <option value="February">February</option>
              <option value="March">March</option>
              ...
            </select>              
            <select>
              <option value="all" selected>Years</option>
              <option value="2011">2011</option>
              <option value="2014">2014</option>
              <option value="2016">2016</option>
              ...
            </select> 
        </div> 

The questions are:

1. I did not add films every month and every year, therefore I need to know which months and which years (independent from each other) exists in the database by reading the column "created_at". And then pass to the view. But I have not idea how to do it using Carbon.
2. How could I grab the selected month and year in the , pass then to the controller and make a dynamic search instead just the current month that I posted at the beginning?

EDIT:

Just to update to somebody who may be useful: I have removed the duplicated months by adding a line to the code apported by Yohanan Baruchel and the code looks now like that:

$available_years_with_months = [];

        $all_year_and_months = DB::table('films')
           ->select('*')
           ->orderBy('films.created_at', 'desc')
           ->get()->each(function($film) use (&$available_years_with_months) {
             $date = Carbon::parse($film->created_at);
             $year = $date->format('Y');
             $month = $date->format('F');
             $available_years_with_months[$year][] = $month;
            $available_years_with_months[$year] = array_unique($available_years_with_months[$year]);

           });

Answer 1

Springtf is for change number range to two.

$year_month_film = DB::table('films')
    ->select('*')
    ->whereMonth('created_at', '=', sprintf("%02d",Carbon::now()->month))
    ->orderBy('films', 'desc')
    ->get();

Answer 2

If you want to get only a list of months that actually have movies you can use the next lines that I wrote for you:

$available_years_with_months = [];

$all_year_and_months = DB::table('films')
       ->select('*')
       ->get()->each(function($film) use (&$available_years_with_months) {
         $date = Carbon::parse($film->created_at);
         $year = $date->format('Y');
         $month = $date->format('F');
         $available_years_with_months[$year][] = $month;
       });