Step 1In a large saute pan heated over medium-high heat until hot, add 2 tablespoons oil. Add the onion and cook, stirring frequently, until the onion begins to soften. Stir in the curry powder, cumin and coriander and cook until the spices are aromatic and begin to toast, 1 to 2 minutes. Add the garlic and ginger, stirring to combine.
Step 2Stir in the ground lamb, salt and pepper. Cook, stirring frequently, until the lamb is lightly browned, 6 to 8 minutes. Taste the lamb and adjust the seasoning if desired. Add the wine and cook, scraping any flavorings from the bottom of the pan. Remove from heat and spoon the meat into a bowl.
Step 3In the same pan, heat the remaining 2 tablespoons oil over medium-high heat until hot. Add the potato and cook, stirring frequently, until it just begins to brown. Stir in the carrot and broth. Cover the pan and steam the potatoes and carrots just until they are crisp-tender, about 5 minutes, stirring occasionally. (Check while stirring to make sure the potato does not stick to the bottom of the pan.) Uncover the pan and add the peas, then the meat mixture, stirring to combine. Stir in the cilantro. Taste again and adjust the seasoning and spices if desired.
Step 4Remove from heat and spread the filling onto a sheet pan, then refrigerate it until the filling is chilled. This makes about 5 cups filling, more than is needed for 12 pies; the filling can be warmed and eaten, added to a soup, stew or other dishes as desired. The filling will keep for up to 4 days; covered and refrigerated.
Step 5Divide the prepared pie dough into 12 even pieces, about 3 ounces each, and shape each into a small disk. On a lightly floured board, carefully roll each piece into a circle about 6 inches in diameter and about one-eighth-inch thick. The dough will be flaky and will probably crack on the edges; without working the dough too much, gently mold the dough with your hands as it's rolled to form as perfect a circle as possible. Carefully set the circle aside and continue rolling until all of the circles are formed.
Step 6Assemble the hand pies: Brush the inside of each circle with a very light coating of beaten egg, brushing all the way to the edge of the circle. Place roughly one-fourth cup of the lamb filling in the center of each circle, slightly off to one side (to make it easier to fold over the dough to form the hand pie), but leaving a 1-inch border around the edge on one side. Carefully -- this can be tricky -- fold over half of the dough, lining the edges up to form a half-circle; you may need to support the dough as it's folded over to keep it from cracking. Gently press the edges down to seal the pie. Trim the edges to clean them up, or gently brush the top of the edge of each pie, then fold the edge in again for a cleaner-looking side. Continue until all 12 pies are formed.
Step 7Place the prepared pies on 2 parchment-lined baking sheets and refrigerate them, uncovered, for 30 minutes. Meanwhile, heat the oven to 400 degrees.
Step 8Remove the chilled pies and brush them with the egg wash. Use a small knife to slash 2 to 3 small steam vents in the top of each pie.
Step 9Bake the pies, 1 sheet at a time (refrigerate the other sheet until ready to bake), on the center rack until the pastry is puffed and golden brown, 20 to 25 minutes. Rotate the pies halfway through baking for even coloring. Cool on a rack. The pies can be served warm or at room temperature.