Pulled pork burger

Name: Pulled pork burger
Prep time: 15 min
Cook time: 5 h
Total time: 5 h 15 min
Cuisine: American
Ingredients: 1 garlic clove; 100 g brown onion, cut into rings (1 cm); 1 sprig fresh rosemary, leaves only; 550 g water; 200 g alcoholic apple cider; ½ tsp sea salt, plus extra to taste; 1 tsp Chicken stock paste (see Tips); 800 g boneless pork shoulder, cut into 5 pieces; 500 g barbecue sauce (see Tips); ground black pepper, to taste; 6 burger buns; 12 iceberg lettuce leaves; tomato ketchup, to serve (see Tips)