In a frying pan over medium heat, sauté the chopped onion and garlic until softened, about 5 minutes. Add grated carrot, minced beef, and cook until browned, stirring frequently.
Stir in the tomato paste, Worcestershire sauce, thyme, and rosemary, season with salt and pepper. Cook for an additional 5 minutes. Remove from heat and let cool for 15 minutes.
In a mixing bowl, combine flour and salt. Gradually stir in warm water and olive oil until a dough forms. Knead the dough for about 5 minutes until smooth. Cover and let rest for 30 minutes.
Preheat the grill or barbecue to medium-high heat.
Roll out the puff pastry on a floured surface to fit your baking dish. Fill the pastry with the cooled beef filling, then cover with another layer of puff pastry, sealing the edges. Cut small slits on top for steam to escape and brush with beaten egg.
Place the pie on the grill and cook for about 30-35 minutes, until golden brown. Cook with the lid closed for optimal heat distribution.
While the pie is grilling, roll out the dough for flatbreads to about 5mm thickness. Grill for 2-3 minutes on each side until puffed and lightly charred.
Let the meat pie rest for 15 minutes before slicing. Serve with flatbreads and a dollop of sour cream, garnished with fresh parsley.
