Season the beef with 1 teaspoon of salt.
Heat the oil in a large pot over medium-high heat. When the oil is hot but not smoking, add the beef. Cook for 4–6 minutes, stirring occasionally, until browned and any liquid has cooked out.
Lower the heat to medium. Add the onions and celery. Cook for 2–3 minutes, stirring frequently.
Add the garlic, ½ teaspoon salt, Italian seasoning, black pepper, and Worcestershire sauce. Cook for 1–2 minutes, stirring often.
Add the butter. Once it melts, add the flour. Cook, stirring, for 1–2 minutes to cook out the raw flour taste.
Stir in the beef broth while gently scraping the bottom of the pot. Stir until the flour mixture dissolves.
Bring the broth to a boil (raise the heat if needed). Then reduce the heat, cover, and simmer the beef mixture for 15 minutes, stirring occasionally.
While the beef simmers, defrost the vegetables following package instructions, cutting the time. (We steamed ours in the bag for 3 minutes.)
Add the vegetables to the pot and raise the heat to bring the broth back to a boil. Once boiling, reduce to medium or medium-low and cook, uncovered, for 10–15 minutes, stirring occasionally until the mixture thickens.
Taste and add more salt if needed. (We added ¼ teaspoon to ours.)
Let the beef filling cool. It will thicken more as it cools.
Preheat the oven to 350°F.