Lightly dust the brisket with flour and sprinkle with pepper. Heat the oil over medium-high heat in heavy pot or roasting pan just large enough to hold the brisket snugly. Add brisket and brown each side of brisket until crusty brown (5-7 min/side).
Remove brisket and set aside. Add onions and cook until browned but not yet carmelized.
Turn off the heat and place the brisket on top of the onions. Add the garlic, carrot, beef broth and beer.
Cover and bake for 3 hours.
Remove from oven and let stand for 30 minutes.
Remove cooled brisket from roasting pan and wrap tightly in aluminum foil. Pour pan juices and onion into a food storage container and cover tightly with a lid. Refrigerate beef and pan juices overnight.
The next day, preheat oven to 350F. Pour pan juices and onion into a 9x13-inch baking dish. Unwrap the brisket, cut away any visible fat, and slice thinly across the grain of the meat. Place brisket slices into the pan juices.
Return to oven and bake until pan juices are thickened and meat is hot, about 45 more minutes.