Preheat oven to 350º F.
Mix first 5 ingredients in a small bowl and rub this mixture over all sides of the brisket.
Melt bacon drippings over medium-high heat in a heavy, large oven-proof pot (large enough to fit brisket). Add brisket to pot and brown, about 5 minutes per side. Transfer Brisket to cookie sheet with rim.
Add 2 cups of broth to pot and bring to a boil; scrape browned bits from bottom. Stir in beer, prunes, bay leaves, and brown sugar; bring to boil.
Place brisket back in pot, with fat side down; scatter onion slices over meat to cover, and add garlic cloves.
COVER pot and place in oven. Braise for 1 hour.
Turn brisket over; return pot to oven UNCOVERED and braise for 30 minutes longer.
Add 2 cups broth. COVER and bake 1 ½ hours more.
Transfer Brisket to a cookie sheet; add remaining cup of Broth to liquid in pot along with mushrooms and carrots.
Return brisket to pot; COVER and return to oven. Braise until meat and carrots are very tender, about 45 minutes.
Slowly add more broth if needed, so vegetables are covered. Cool slightly then refrigerate uncovered until cold.
Once completely cold, cover and keep chilled at least 1 to 2 days.
On the day of serving: Preheat oven to 350ºF. Spoon off any solid layer of fat from surface and discard.
Transfer brisket to cutting board and thinly slice crosswise. Place Brisket slices in large roasting pan; leaving vegetables and broth in the pot.
Bring the pot of vegetables to a boil. Whisk in whole grain mustard and vinegar. Season to taste with salt and pepper. Slowly add more vinegar to taste.
Pour pan juices and vegetables over brisket.
Cover pan tightly with heavy-duty foil, and cook in oven until brisket slices and vegetables are heated through, about 1 hour and 15 minutes.
Serve meat with vegetables and sauce.