Heat the oil in a large skillet over medium heat. Add the onion and cook, stirring often, until softened, about 3 minutes.
Add the ground beef. Break it into very small crumbles with a spoon and cook until no pink remains, about 5 to 6 minutes. Carefully spoon off excess fat if there is more than a small amount in the skillet.
Sprinkle the flour over the beef and stir for 1 minute. Stir in the tomato paste, Worcestershire sauce, Vegemite or bouillon paste, salt, pepper, and thyme, if using.
Gradually stir in the beef broth, scraping up any browned bits from the bottom of the skillet. Bring the mixture to a gentle simmer and cook, stirring frequently, until the gravy is thick and glossy and the filling holds its shape on a spoon, about 6 to 8 minutes.
Taste and adjust the seasoning if needed. Let the filling stand for 5 minutes to thicken further before using.
For individual meat pies, spoon the filling into pastry-lined pie tins, leaving a small border. Add pastry tops, seal and vent them, then bake according to the directions for your store-bought pastry or your chosen homemade crust recipe. Serve with tomato sauce or ketchup, if desired.