Make the spice paste: Pulse 2 tablespoons salt, 1 tablespoon plus 1 1/2 teaspoons pepper, the sugar, bay leaves, spices, garlic, vinegar, and mustard in a food processor.
Make the brisket: Rub spice paste all over brisket. Transfer to a 9-by-13-inch baking dish. Cover, and refrigerate overnight.
Preheat oven to 350 degrees. Combine beer and juice. Top brisket with onion, and surround with beets. Pour in 1 1/2 cups beer mixture. Bake, covered with parchment-lined foil, basting occasionally, until tender, 3 hours to 3 hours 15 minutes.
Once brisket has baked for 2 hours, place cabbage and carrots in a 2-quart baking dish. Top with remaining beer mixture. Season with salt. Bake, covered with parchment-lined foil, until tender, about 1 hour.
Slice brisket; return to liquid, and serve with vegetables.