Heat olive oil in a large pot over medium-high heat. Add the chopped onion and celery. Cook for about 5 minutes until the vegetables start to soften. Stir in minced garlic, Italian seasoning, and dried thyme, and cook for 30 seconds.

Add the lean ground beef to the pot. Break it up as it cooks and stir until the meat is browned, about 8 minutes.

Sprinkle the flour over the meat and vegetable mixture. Stir continuously for 1 to 2 minutes to coat the ingredients and lightly toast the flour. Mix in the tomato paste until well combined.

Pour in the beef broth and add Worcestershire sauce. Stir in the cubed potatoes and diced carrots.

Bring the mixture to a boil, then reduce heat to a simmer, cover, and cook for 30 minutes until the vegetables are tender. If the stew becomes too thick, add a bit more broth.

Stir in the frozen peas (if using) and season with salt and pepper to taste. Let cook for an additional 5 minutes before serving.

Ladle the hamburger stew into bowls and serve hot, garnished with parsley. Enjoy with a side of whole-grain bread or a light salad for a balanced meal.