Preheat your oven to 400°F (200°C). Lightly grease a pie dish if necessary, and prepare your vegetables by chopping the onion, dicing the carrots, and mincing the garlic. Make sure the pastry is thawed but still cool enough to handle easily.
Heat the olive oil in a large skillet over medium heat. Add the ground beef and cook for approximately 6–8 minutes, breaking it into small pieces with a wooden spoon until browned. Drain excess fat if necessary.
Add the chopped onion, carrots, and minced garlic to the skillet. Cook for another 5–7 minutes, stirring occasionally, until the vegetables begin to soften. Stir in the frozen peas and mix everything thoroughly.
Add the tomato paste, Worcestershire sauce, dried thyme, salt, and black pepper. Pour in the broth and stir well. If you prefer a thicker filling, mix the optional flour with a little cold water before adding it to the skillet.Simmer for approximately 8–10 minutes until the vegetables are tender and the sauce has thickened. Allow the mixture to cool slightly before assembling the pie. Roll out one pastry sheet and place it inside your pie dish, gently pressing it against the bottom and sides. Trim any excess pastry, leaving enough around the edges to seal the pie later.
Spoon the cooled meat and vegetable mixture evenly into the pastry-lined dish. Spread it out gently, leaving a small border around the edges. Avoid adding excess liquid because it can make the bottom crust soggy.
Place the second pastry sheet over the filling, or use it to create a decorative top, depending on your preferred design. Seal the edges by pressing them together with your fingers or a fork.Cut small pastry shapes for the eyes, nose, and eyebrows. Use small pieces of pastry or carefully positioned black olives for the eyes. Shape a curved strip of pastry into a smile and attach the decorations gently. Make a few small vents if needed to release steam. Brush the pastry lightly with beaten egg to encourage an attractive golden finish. Take care not to cover the face details too heavily, as you want the design to remain recognizable after baking.
Place the pie in the preheated oven and bake for approximately 35–40 minutes, or until the pastry is puffed and golden brown and the filling is piping hot. If the decorations brown too quickly, loosely cover those areas with foil.
Remove the pie from the oven and allow it to rest for 10 minutes before slicing. This helps the filling settle and makes serving easier. Cut into portions and serve warm with salad, steamed vegetables, or your favorite side dish.