Red pesto minestrone soup

Name: Red pesto minestrone soup
Ingredients: 2 tbsp olive oil; 1 onion finely chopped; 1 carrot finely chopped; 1 celery stick finely chopped; ½ Savoy cabbage leaves shredded and the core finely chopped; 3 garlic cloves finely chopped; ½ tsp chilli flakes (optional); 1 tsp dried mixed herbs; 1 tbsp tomato purée; 1.5 litres low-salt vegetable stock; 4 tbsp red pesto (check it’s vegetarian if needed); 100g dried lasagne sheets roughly snapped; 20g parmesan or vegetarian alternative, grated, to serve