Grab a large bowl and add your diced garlic, salt and paprika.
Crush down the garlic into the paprika and salt mixture to release the juices from the garlic.
Pre-heat a heavy bottom pan over the stove on high heat.
Now grab your brisket and trim off any excess fat. Some fat is fine.
Take your brisket and press it into your spice mixture making sure to coat the whole brisket well. You may have to pick up some of the spice mixture and press it on to the meat.
Once your pot is pre-heated, add your olive oil.
Now add your brisket and sear all sides well. If you have any remaining spice mixture that fell off the meat then make sure to throw that into the pot too. You want all of the spice mixture in your pan.
Once you have seared all sides of the meat, remove from the pan and place on a large plate and set aside.
Add a little water (about ½ cup) to your pan to deglaze it. Let it bubble up and scrape down any brown bits from the bottom.
If you are using the slow cooker
Add your seared brisket to the slow cooker.
Pour the liquid from deglazing over top of your brisket. You should have enough liquid to come up about ½ inch up the side of your pan. If you do not, add more water until it does.
Place the lid on the slow cooker and set it to low.
Cook for 6-7hours or until the brisket is almost falling apart. This will depend on your cut of brisket and slow cooker how long it takes.
Now add your potatoes and carrots and coat them with the juices in the pot.
Cook for another hour.
Once the brisket is falling apart and tender and the vegetables are cooked, taste for seasoning.
If you are using the oven
Pre-heat your oven to 350 degrees
Add your seared brisket to a roasting pan.
Pour the liquid from deglazing over top of your brisket.
Top your brisket with aluminum foil and bake for 3 hours, making sure to baste the brisket every 45 minutes.
After 3 hours, add your potatoes and carrots to the brisket and coat them well with the juices from the pan.
Cover and cook for another hour.
After an hour, with a fork, check to see if the brisket is ready by poking it. If it slightly falls apart it is ready. Pierce the potatoes and carrots as well to check for doneness.
Grab a large platter and gently lift out your brisket and place it in the center of the platter.
Now scoop out your potatoes and carrots and place along the sides of the brisket.
Scoop out some of the pan juices from the pan and pour over the brisket and potatoes.