Call to PHP static function using PDO

Question

I have a Abstract class for my database Database.php:

abstract class Database {
private $host      = DB_HOST;
private $user      = DB_USER;
private $pass      = DB_PASS;
private $dbname    = DB_NAME;

private $dbh;
private $error;

private $stmt;

public function __construct(){        
    // Set DSN
    $dsn = 'mysql:host=' . $this->host . ';dbname=' . $this->dbname;
    // Set options
    $options = array(            
        PDO::ATTR_PERSISTENT    => true,
        PDO::ATTR_ERRMODE       => PDO::ERRMODE_EXCEPTION            
    );
    // Create a new PDO instanace
    try{
        $this->dbh = new PDO($dsn, $this->user, $this->pass, $options);
    }
    // Catch any errors
    catch(PDOException $e){
        $this->error = $e->getMessage();
    }
}

public function query($query){        
    $this->stmt = $this->dbh->prepare($query);
    }
}

Then I have a Recipe class that extends Database with a static function:

class Recipe extends Database{

private $id;
private $slug;
private $title;     

public function __construct {
       $this->id=$id;
       $this->slug=$slug;
   $this->title=$title;
       parent::__construct();
    }

    public static function getAll () {      

   self::query('select * from recipes order by id');        
   $rows = self::resultset();       
   $recipes=array();
   foreach ($rows as $row){// show}
    }

Finally in my index.php:

$recipes=Recipe::getAll();

What's the correct way to do this?

I don't want to create a instance of Recipe each time I need to do a SQL query like this method:

$recipes=new Recipe();
$recipes->getAll();

then in recipes class:

$this->query('select * from recipes order by id');      
$rows = $this->resultset();

Thanks!!