Dredge the Beef: Pat the beef chuck cubes thoroughly dry with paper towels. Toss in a medium bowl with 1/3 cup flour, 1 teaspoon kosher salt, and 1/2 teaspoon black pepper until evenly coated.

Sear in Batches: Heat 1 tablespoon olive oil and 1 tablespoon butter in a heavy 6-quart Dutch oven over medium-high heat. Sear half the beef cubes undisturbed for 3 to 4 minutes per side until a deep, dark mahogany crust forms. Transfer to a plate and repeat with remaining oil, butter, and beef. Set seared beef aside.

Sauté Aromatics & Deglaze: Lower heat to medium. Add chopped onion and celery to the pan drippings and sauté for 4 minutes until softened. Stir in minced garlic and tomato paste, cooking for 1 minute until fragrant. Pour in balsamic vinegar and 1/2 cup beef bone broth, using a wooden spoon to scrape up all the rich caramelized brown bits (fond) from the bottom of the pot.

Simmer the Beef: Return seared beef and resting juices to the pot. Pour in the remaining beef bone broth, Worcestershire sauce, smoked paprika, fresh thyme sprigs, rosemary, and bay leaves. Bring to a boil, then reduce heat to low, cover tightly with the lid, and simmer gently for 1 hour and 15 minutes until beef begins to soften.

Add Root Vegetables: Stir in halved Yukon gold potatoes and sliced carrots. Return the lid and continue simmering on low heat for 45 to 50 minutes until both the beef and vegetables are fork-tender and the gravy is thick and glossy. (If using a Slow Cooker: transfer seared beef, deglazed aromatics, broth, herbs, potatoes, and carrots to slow cooker; cook on LOW for 7-8 hours or HIGH for 4 hours).

Finish with Sweet Peas: Discard herb stems and bay leaves. Stir in frozen green peas and simmer uncovered for 5 minutes until tender and vibrant green. Taste and adjust salt and pepper as needed.

Garnish & Serve: Ladle hot, steaming stew into wide shallow bowls. Sprinkle generously with freshly chopped parsley and serve immediately with thick slices of warm crusty sourdough bread.