@Defrag That almost worked I just needed to tweak it
$browser->check("input[name='department_id[]']");
This will select the first one however it got me thinking how to select say the first third and fifth ones.
I think the following should work
// View
@foreach ($departments as $department)
<tr>
<td>
<input type="checkbox" name="department_id[{!! $department->id !}}]" value="{!! $department->id !}}" />
</td>
<td>{!! $department->department !!}</td>
</tr>
@endforeach
// Test
// You could loop over or be explicit about which ones you want to select
$browser->check("input[name='department_id[" . $department->id . "]']")