Preheat oven to 180°c - 350°f.
Place the diced beef into a large mixing bowl with the plain (all-purpose) flour and mix to combine, shaking off any excess flour. Place on a plate.
Place a large high rimmed pan or pot over high heat. Add in 1 Tbsp (20ml) of olive oil and sear the floured beef in batches for 4-5 minutes or until golden all over and a slight crust has formed. Remove and set aside.
Reduce heat to medium-high, add in the remaining olive oil along with the onions, carrots, celery garlic and thyme. Saute for 3 minutes, mixing regularly.
Add in the wine or beef stock (see notes) and deglaze for 1 ½ minutes, season to taste and mix well.
Add the seared beef back in along with the balsamic vinegar and stock, check for seasoning, adjust accordingly, mix well and bring to a simmer. Place on a lid or wrap the pan or pot in foil if you don't have a lid, transfer it to the preheated oven and braise for 1 ½ hours. Remove the lid after 1 ½ hours and allow it to braise uncovered for a final 30 minutes before removing it from the oven.
Serve in bowls, plates or whatever you like, garnish with chopped flat-leaf parsley. Dig in.