Microwave water and mushrooms in a covered bowl until steaming, about 1 minute. Strain mushrooms through a fine-mesh strainer lined with a coffee filter, reserving ¼ cup liquid. Chop the mushrooms and set aside.
Preheat oven to 325°F and adjust the rack to the lower-middle position. Pat beef dry with paper towels, then season with salt and pepper. Heat 2 tablespoons olive oil in a Dutch oven over medium-high heat until shimmering. Brown half the beef on all sides (8–10 minutes) and transfer to a bowl. Repeat with remaining beef and 1 tablespoon olive oil.
Reduce heat to medium and add salt pork, carrots, onions, tomato paste, and garlic. Cook, stirring occasionally, until lightly browned (about 2 minutes). Stir in flour and cook for 1 minute. Gradually whisk in wine, scraping up browned bits. Add chicken broth, beef, and juices. Bring to a simmer.
Add mushrooms, reserved liquid, orange zest, anchovies, thyme bundle, and bay leaves. Submerge the beef in the liquid, partially cover the pot, and transfer to the oven. Cook until beef is tender (2 1/2–3 hours).
Discard salt pork, thyme, and bay leaves. Skim fat from the stew's surface. Stir in tomatoes and olives, and let sit for 2 minutes until heated through. Adjust the consistency with extra chicken broth if needed. Stir in parsley, season with salt and pepper, and serve.