Heat olive oil in a large skillet over medium heat. Add the chopped onion and garlic, and sauté until softened.

Add the minced beef to the skillet and cook until browned, breaking it apart with a spoon.

Stir in the diced carrots, tomato paste, Guinness, Worcestershire sauce, thyme, salt, and pepper. Bring to a simmer and cook for 30 minutes until thickened.

In a mixing bowl, combine the flour and salt. Add the cold butter and rub it into the flour until the mixture resembles breadcrumbs.

Add cold water, one tablespoon at a time, mixing until the dough comes together. Wrap in plastic wrap and chill for 30 minutes.

Preheat the oven to 200°C (400°F). Roll out the pastry on a floured surface to fit your pie dish.

Fill the pie dish with the beef filling, then cover with another layer of pastry. Seal the edges and cut slits in the top to allow steam to escape.

Brush the top with beaten egg and bake in the preheated oven for 30-35 minutes until golden brown.