Place onion, garlic, celery, carrot, sugar and oil into a large fry pan and cook on a medium heat until starting to brown a little. Deglaze the pan with the fish sauce and transfer entire mixture to your slow cooker.
Toss the beef cheeks in the seasoned flour and quickly seal in the fry pan one at a time. Add more oil if needed.
Deglaze the pan each time with a little of the red wine.
Transfer beef cheeks to slow cooker. Add remaining ingredients to slow cooker, except carrots and mushrooms and cook on the low setting for 6-12 hours.
(Depending on the size of the beef cheeks, check for tenderness after about 6 hours. If falling apart they are done.)
In the last hour, add carrots and mushrooms, ensuring they are underneath the liquid so as to cook well.
Serve with plenty of mash or soft polenta and sprinkled with chopped parsley.