Spray a frying pan with low-calorie cooking spray and add the onion and carrot and fry for 4 minutes. Add the mushrooms and garlic and fry for a further 4 minutes.
Once the vegetables have begun to soften, add the beef mince and fry until browned on all sides. This should take about 2 minutes.
Add the chopped tomatoes, tomato puree, Henderson's relish, balsamic vinegar and stir. Crumble in the stock cube and lower the heat, simmer for 10 minutes. The bolognese should be rich and thickened.
Split the cheese into 4. Add 1 tortilla wrap to a clean frying pan and sprinkle over a quarter of the cheese. Add half the bolognese to the wrap, spreading out to cover while leaving a 1cm gap around the edge. Set the pan on a medium heat and fry for 2 minutes; the wrap should be golden brown and cheese melting.
Sprinkle over another quarter of cheese over the top of the bolognese and add another tortilla wrap. Gently press down and using a spatula or fish slice flip the quesadilla over, so that the cooked wrap is now on the top. Fry for a further 2 minutes. Remove from the pan and repeat with the remaining bolognese and wraps.
Once both quesadillas are cooked, cut them in half and then into quarters. Serve with an accompaniment of your choice!