Preheat oven to 400 degrees. Place brisket in a large, heavy-bottomed roasting pan; season with salt and pepper. Heat oil in a large straight-sided skillet over medium-high; add onions, 2 teaspoons salt, and 1/2 teaspoon pepper and cook, stirring, until onions are translucent, 3 to 4 minutes. Add broth, chili sauce, brown sugar, and vinegar; bring to a boil.
Place roasting pan over two burners; pour in broth mixture and return to a boil. Cover pan with parchment-lined foil and roast in oven 30 minutes. Reduce oven temperature to 350 degrees; roast 1 hour, 15 minutes more. Add carrots and potatoes and continue roasting, uncovered, tossing vegetables occasionally, 1 hour. Baste meat with pan juices and continue to roast, basting and tossing vegetables occasionally, until meat is tender but not falling apart, and potatoes and carrots are cooked, about 1 hour more.
Transfer brisket to a cutting board. Let stand 10 minutes, then slice and serve with sauce, vegetables, and parsley.
