Using a paring knife and your finger, make small slits all over the brisket and stuff each slit with a piece of the garlic. Season the brisket with the salt.
Heat a small Dutch oven or a saucepan just slightly larger than the brisket over medium-high heat and add the vegetable oil. When the oil is hot, add the brisket to the pan and brown well on both sides. Remove the meat from the pan and set aside.
Add the peppers and onions to the pan and cook, stirring often, until tender, about four minutes.
Season the brisket on both sides with 2 tablespoons of the Rib Rub and return the brisket to the pan, positioning the sautéed vegetables over the top of the meat. Add the stock, beer and the remaining tablespoon of Rib Rub.
Bring to a simmer, cover and place in the oven.
In a small bowl combine the onion powder, garlic powder, ketchup, chili sauce and brown sugar. Remove brisket from oven after one and a half hours and add the ketchup mixture. Return the brisket to the oven and continue to cook, covered, for another hour and a half or until the meat is fork tender.
Allow the brisket to cool in the cooking liquid and refrigerate overnight. To serve the brisket, remove any congealed fat from the top of the liquid and discard.
Remove the brisket from the pan and set aside.
Return the pan to the stovetop, bring liquid to a boil and continue to cook until liquid is reduced to sauce consistency.
While the sauce is reducing, slice the brisket crosswise against the grain.
Return the brisket back to the pan briefly until warmed through, then serve immediately.