First take your brisket remove any excess fat on meat(leave a little for flavoring).
Now take a cast iron pan or dutch oven pot heat up on med-hi heat with some vegetable oil. While heating that take your dried seasonings and rub over brisket.Then put into pan green peppers & onions and brisket sear both sides of meat till browned(about 5 minutes a side).
Now add about 3 cups of water(just enough to cover the meat to cook.Add tomato sauce. Now simmer for 1 1/2 hours.
Now take out your brisket and slice thinly across the grain and then put back into pot.Cook for another 1 1/2 hours.After about 1/2 hour add your potatoes and carrots.Cook till tender and put them into a separate bowl. Then take out your meat and put on platter.Take your stock"gravy"in pot and add some tickening agent(whatever you prefer to use, I use Wondra with cold water) to pot to make a thicker gravy. Pour over your brisket and serve.