Pat all meat pieces dry with paper towels. In a large bowl combine the flour, 1 1/2 tsp kosher salt and 1/2 tsp black pepper. Toss the beef and pork in the seasoned flour to coat; set chicken aside unfloured (it will be added later to avoid overcooking).

Brown meats

Heat a large heavy-bottomed pot or Dutch oven over medium-high heat and add 2 tablespoons neutral oil. When shimmering, add beef in a single layer (work in batches if needed) and brown on all sides, about 6–8 minutes. Remove to a plate. Add remaining 1 tablespoon oil and the butter; when foaming, sear pork until browned, about 4–5 minutes. Remove pork with beef. Reduce heat to medium and briefly brown chicken pieces, about 2 minutes per side (they should be golden but not cooked through). Remove and set all meat aside.

Aromatics & Vegetables

Lower heat to medium. Add the diced onion to the empty pot and cook, stirring occasionally, until translucent and beginning to brown, 6–8 minutes. Add the carrots and celery and cook 4–5 minutes more to soften. Stir in the minced garlic and cook 30–45 seconds until fragrant.

If using mushrooms, add them now and sauté until they release liquid and begin to brown, 4–5 minutes. Return the browned beef and pork to the pot and add the halved potatoes.

Liquids & Seasonings

Stir in the tomato paste and cook 1 minute to remove raw flavor. Pour in the red wine to deglaze the pot, scraping up browned bits from the bottom with a wooden spoon. Allow wine to reduce by half, about 2–3 minutes. If not using wine, add 1/2 cup of the beef broth and scrape up the bits.

Add the remaining beef broth, bay leaves, thyme sprigs, Worcestershire sauce, soy sauce (if using), and the remaining 1/2 tsp salt and 1/2 tsp pepper. Bring to a gentle simmer. Nestle the chicken pieces into the liquid so they are mostly submerged.

Cover partially with a lid and simmer gently on low for 45–55 minutes, stirring occasionally, until beef and pork are tender and potatoes are cooked through. If the liquid reduces too much, add up to 1/2 cup more broth or water.

Finishing & Garnish

Check seasoning and remove thyme sprigs and bay leaves. If you prefer a slightly thicker stew, make a slurry by whisking cornstarch with cold water, then stir the slurry into the simmering stew and cook 2–3 minutes until slightly thickened.

Stir in chopped parsley and lemon zest if using. Taste and adjust salt and pepper to taste. Let the stew sit off heat 5 minutes to meld flavors before serving.

Serve hot in bowls, spooning both meat and vegetables with plenty of braising liquid. Garnish with additional parsley if desired.