Roughly dice the beef into 3cm chunks, trimming off any excess fat. Place into a bowl and cover with flour, salt and pepper. Toss to coat evenly and set aside.
Roughly chop the onions into large wedges. Dice the carrots and celery into large chunks of about equal size. Halve or quarter the mushrooms so they are a similar size to the other vegetables. Roughly chop the potatoes into large chunks and set aside in a bowl of cold water.
Place a large oven-proof pot or casserole on high heat. Add the olive oil and brown the beef until lightly coloured on all sides. If any excess flour sticks to the pot, add a dash of the red wine and stir to loosen. Once the meat is browned, transfer to a bowl and set aside.
Preheat the oven to 150ºC and adjust the oven racks to accommodate the casserole so it can cook in the centre of the oven.
Reduce the heat to medium-high and add some more olive oil to the pot. Add the onions, carrots, celery, thyme and bay leaves. Cook for about 5 minutes, stirring regularly, until the onions have softened. Add the tomato purée and mushrooms. Stir to combine and cook for a further 2-3 minutes. Add the red wine, bring to a simmer and bubble for 2-3 minutes to cook off the alcohol. Add the beef and any juices back into the pot. Season well with salt and pepper then top with the beef stock until the contents are covered by about 3-4cm of liquid. Bring the pot to the boil then cover with a lid and transfer to the oven.
Cook in the oven for 3 hours, stirring about once every hour.
Remove the pot from the oven and add the potatoes. Taste the casserole sauce and season as necessary. Return the pot to the oven with the lid askew and cook for a further 60 minutes, until the potatoes are cooked and the sauce has thickened. If after 60 minutes the sauce needs to be thickened further, remove the lid and cook for another 30 minutes, stirring occasionally.
When the stew is ready, remove from oven and let stand for 10 minutes. Stir about half the chopped parsley through the casserole. Serve in bowls and garnish with the remaining parsley and a side of crusty bread.