In a spacious skillet, warm the olive oil over medium heat. Stir in the finely diced onion along with a small pinch of salt. Sauté for about 4-5 minutes, or until the onion is tender and translucent.
Stir in the ground ginger, granulated garlic, cumin seeds, and red-pepper flakes.
Add the ground lamb and cook, breaking it up with a spoon, until browned and fully cooked, about 5-7 minutes. Season with salt to taste.
Add the cubed potatoes and cook for another 5 minutes, stirring frequently.
Stir in the frozen peas and cook for another 3-4 minutes until the potatoes are tender.
Pour in the cornstarch and water mixture and cook for 1-2 minutes until the mixture thickens slightly.
In a large bowl, whisk together the flour, salt, and ground turmeric.
Add the chilled vegetable shortening and use your fingers or a pastry cutter to blend it into the flour until the mixture resembles coarse crumbs.
Gradually add cold water, 1 tablespoon at a time, until the dough comes together. It should be soft but not sticky. Form the dough into a ball, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
Preheat your oven to 375°F (190°C).
On a lightly floured surface, roll out two-thirds of the dough into a circle large enough to line a 9-inch pie dish.
Spoon the cooled lamb and potato filling into the pie shell, spreading it evenly.
Roll out the remaining dough into a circle large enough to cover the top of the pie. Pinch the edges together to seal and crimp as desired.
Brush the top of the pie with the beaten egg for a golden, glossy finish.
Place the pie on a baking sheet and bake in the preheated oven for 35-40 minutes, or until the crust is golden brown and the filling is bubbling.
Allow the pie to cool for a few minutes before slicing. Serve warm with your favorite chutney or a side salad for a complete meal.