Cut the lamb into uniform cubes. In a large skillet over medium heat, brown the lamb pieces for 5–7 minutes. Add onions and carrots; stir for another 5 minutes.

Pour in the savory broth and sprinkle in the herbs. Let it simmer on low for 1–1.5 hours until the lamb is tender.

Combine flour and cold butter in a bowl. Mix until it resembles coarse crumbs. Gradually add ice-cold water until dough holds together.

Shape the dough into a ball, wrap in plastic, and refrigerate for 30 minutes.

Preheat the oven to 400°F (200°C). Roll out half the pastry and fit it into the pie dish. Spoon the filling in evenly.

Cover with the second half of the pastry, pinch edges to seal, and cut slits for steam.

Prepare an egg wash by whisking egg and water. Brush over the top crust. Bake for 45-50 minutes until golden brown.

Let the pie rest for 10 minutes before serving. Enjoy warm with mashed potatoes or salad.