Preheat oven to 350°F.
Microwave ½ cup broth and mushrooms for 1 minute, let sit 5 minutes, then drain and chop mushrooms.
Heat olive oil in a Dutch oven over medium heat. Cook onion for 5 minutes.
Add garlic and cook 1 minute. Add tomato paste, anchovies, and five-spice powder, cook for 3-4 minutes.
Add wine, increase heat, and simmer until nearly dry, 2-4 minutes.
Stir in chopped tomatoes with juice, remaining broth, mushroom liquid, and chopped mushrooms. Bring to a simmer.
Season beef with ½ tsp salt and pepper, add to pot. Cover and cook in oven for 1 hour.
Uncover and cook until beef is tender, 1 to 1¼ hours longer.
Remove from oven, transfer beef to cutting board, and cool for 5 minutes.
Shred beef, discard fat, skim sauce, and return beef to pot. Season to taste.