In a large pot over medium heat, brown the ground beef until fully cooked. Drain excess fat if necessary. Add the diced onion and garlic, cooking until the onion is translucent, about 3-4 minutes.
Stir in the carrots, celery, thyme, salt, and pepper. Cook for another 5 minutes until the vegetables begin to soften.
Pour in the beef broth and Worcestershire sauce. Bring to a simmer, then reduce heat and let it cook for 10 minutes. Stir in the frozen peas.
While the stew simmers, prepare the dumplings. In a mixing bowl, combine the flour, baking powder, and salt. Add the milk and melted butter, stirring until just combined.
Drop spoonfuls of the dumpling batter onto the simmering stew. Cover the pot and let the dumplings steam for about 15 minutes without lifting the lid.
Once the dumplings are fluffy and cooked through, serve the beef and dumplings hot, garnished with fresh parsley.