Preheat the oven to 180C/160C Fan/Gas 4.
Preheat a casserole dish on the hob, then spray with oil. Add the beef in batches, cooking each batch until browned all over and spraying with more oil as needed. Transfer the beef to a plate using a slotted spoon and set aside. Add a little stock to the dish, turn the heat up to high, and deglaze by scrubbing off the cooked-on bits with a spatula.
Turn down the heat and spray the dish with more oil. Add the onion and cook until softened. Add the garlic and cook for 1-2 minutes. Add the celery and finely chopped carrot and cook for 3-4 minutes. Stir in the tomato purée and balsamic and cook for 2-3 minutes more. Return the meat to the pan and stir in the rest of the stock, then bring to the boil.
Put the dish in the oven (without a lid) and cook for 1 hour.
Add the parsnip, butternut squash and carrot chunks, put the lid on the dish and cook for another 30 minutes.
For the dumplings, put the flour in a mixing bowl with the salt and pepper. Mix in the herbs. Add the egg and oil and mix, adding just enough cold water to bring it together as a dough (about 4 tbsp). Be careful not to add too much water as this will make the dumplings heavy. Knead the mixture a little.
Shape into eight golf-ball-sized pieces and put on top of the stew, pushing down a little to coat in the juices. Cover with the lid and return to the oven for 15 minutes, then remove the lid and cook for a further 15 minutes.
When the dumplings are golden-brown, lift them out of the stew into serving bowls and stir the stew (the squash will be very tender, which will thicken and flavour the sauce). Serve immediately.