Slice onion and celery and put in resealable bag.
Mince garlic and throw into separate resealable bag.
Throw thyme and bay leaves into separate resealable bag.
Set up dutch oven for frying with about 18 briquettes.
Once hot, add vegetable oil and brown brisket on all sides.
Remove brisket to small plate or bowl and pour oil out of dutch oven.
Add garlic, thyme, bay leaves, tomatoes, tomato paste, salt, pepper and wine. Stir until the tomato paste is mixed in.
Slightly crush tomatoes with mixing spoon.
Add onions and stir.
Place brisket neatly on top and spoon some of the wine over it.
Cover and gently simmer for 3 1/2 to 4 hours (probably don't need more than 6 briquettes at a time).
Every 30-45 mins spoon wine, onions and tomatoes over the brisket.
Be certain your charcoal does not burn out.
After braising period, nestle carrots around the brisket.
Add 18 briquettes to lid and prop lid open slightly so that steam can escape.
Cook for an additional 30 minutes, or until carrots are tender.