Heat the olive oil in a large skillet over medium heat. Add the cubed beef and cook until browned on all sides. Remove the beef from the skillet and set it aside.

In the same skillet, add the diced onion, carrots, and celery. Cook until the vegetables are softened, about 5 minutes. Add the minced garlic and cook for an additional 1 minute.

Sprinkle the flour over the vegetables and stir to coat. Slowly pour in the beef broth, stirring constantly to avoid lumps. Add the Worcestershire sauce, thyme, rosemary, salt, and pepper. Return the beef to the skillet and stir to combine. Simmer for 10-15 minutes, or until the gravy has thickened.

Preheat your oven to 375°F (190°C). Divide the beef and gravy mixture evenly among four oven-safe ramekins or small baking dishes.

Cut the puff pastry into four circles, large enough to cover the tops of the ramekins. Place a pastry circle over each ramekin and press the edges to seal. Brush the tops with the beaten egg for a golden finish.

Place the ramekins on a baking sheet and bake for 20-25 minutes, or until the pastry is golden brown and puffed. Allow the pies to cool for a few minutes before serving.