Australian Beef and Beer Pie

Name: Australian Beef and Beer Pie
Cuisine: American, Australian
Ingredients: 500g beef chuck or stewing beef, diced into 2 cm cubes; 1 large onion, finely chopped; 2 garlic cloves, minced; 1 large carrot, diced (optional); 1 tbsp plain flour; 1 tbsp tomato paste; 1 cup dark beer (like stout or ale); 1 cup beef stock; 2 tbsp olive oil; 1 tsp fresh thyme leaves (or ½ tsp dried); Salt and pepper to taste; 1 sheet shortcrust pastry (for the base); 1 sheet puff pastry (for the top); 1 egg, beaten (for egg wash)