Preheat your oven to 325° F.
Liberally season the brisket with salt and pepper.Some cooks also like to dust it with flour for a crisper external texture and to add a modicum of thickening to the fluid but this is not absolutely necessary.
In a large, heavy, oven-proof Dutch oven heat the oil. Sear the brisket until well browned on each side. Remove the meat and set aside.
Sauté the onion, adding more oil if necessary. When the onion is almost done add the garlic and sauté one more minute.
Add the wine and deglaze. Reduce the wine to about half.
Add the remaining ingredients except the potatoes and carrots. Add additional salt and pepper.
Return the meat to the pot. Cover and place in the oven for 2 hours and 15 minutes.
Then add the potatoes and carrots.
Check the fluid level in the pot. If it looks low add some more stock.
Cook another 45 minutes or until the vegetables have reached your desired tenderness.