I've been trying to figure this out for a while before I cracked it:

Users Controller

use Illuminate\Foundation\Auth\SendsPasswordResetEmails;

class Users extends Controller
{

    use SendsPasswordResetEmails;

    public function resetPassword(Request $request, $id)
    {
        $this->sendResetLinkEmail($request);

        // your response
    }

The form I used in my view is

<form id="password-reset-form" action="/users/{{ $user->id }}/reset-password" method="put">
   {{ csrf_field() }}
   <input type="hidden" name="_method" value="put">
   <input type="hidden" name="email" value="{{ $user->email }}">
   <button type="submit">Reset Password</button>
</form>

Then all you need is a route

Route::put('users/{id}/reset-password', 'Users@resetPassword');