In a large pot over medium heat, sauté diced onions and carrots in olive oil for 5-7 minutes until softened. Add cubed lamb or mutton, browning it on all sides for 8-10 minutes. Stir in thyme, rosemary, parsley, and savory broth, bringing to a gentle simmer. Cover and let cook for approximately 1 hour or until meat is tender.

While filling simmers, roll out pastry dough on a lightly floured surface to about 1/8 inch thick. Cut dough slightly larger than pie dish and transfer into the dish, pressing gently into the edges.

Once filling is tender, taste and adjust seasoning if necessary. Spoon the mixture evenly into the prepared pastry crust, leaving a little room at the top.

Cover filled pie with a second layer of pastry, crimping edges to seal. Cut several slits in top for steam to escape. Brush with beaten egg. Preheat oven to 375°F (190°C) and bake for 40-45 minutes or until crust is golden brown.

Allow pie to cool for 10 minutes before slicing. Serve warm with buttery mashed potatoes or a crisp green salad.