Pat the beef dry, then season with 1 tsp salt and the black pepper. Toss with the dredging flour to coat.
Heat olive oil in a large heavy pot over medium-high heat. Brown beef in batches until nicely seared.
Lower heat to medium. Sauté onion, carrots, and celery in the pot until softened, about 5 minutes.
Stir in garlic and tomato paste. Cook until fragrant and darkened slightly, 1 to 2 minutes.
Return beef to the pot. Pour in beef broth and Worcestershire; add thyme and crushed bay leaf. Scrape up browned bits.
Bring to a simmer, then cover and cook gently over low heat until beef is tender, about 50 minutes.
Whisk dumpling flour, baking powder, and remaining 1/2 tsp salt in a bowl. Stir in milk, melted butter, and parsley.
Check seasoning on the stew and adjust with salt if needed. Keep it at a gentle simmer.
Drop heaping tablespoons of dumpling batter onto the simmering stew, spacing evenly across the surface.
Cover tightly and cook without lifting the lid for 15 minutes, until dumplings are puffed and cooked through.
Rest 5 minutes off heat. Ladle stew into bowls with dumplings on top and serve hot.