1. In a large skillet, cook the beef over medium-high heat until browned on all sides, about 8 minutes. Remove from heat and set aside.

2. In the same skillet, cook the onions over medium heat, stirring occasionally, until caramelized, about 20 minutes. Remove from heat and set aside.

3. In a food processor, combine the flour, salt, and black pepper. Add the cold butter and pulse until the mixture resembles coarse crumbs. Add the ice water and pulse until the dough just begins to come together.

4. Divide the dough in half and shape each half into a disk. Wrap in plastic wrap and refrigerate for at least 1 hour.

5. Preheat the oven to 375°F.

6. On a lightly floured surface, roll out one disk of dough into a 12-inch circle. Transfer to a 9-inch pie plate.

7. Layer the beef and caramelized onions in the pie crust. Roll out the remaining dough into a 12-inch circle and place on top of the filling. Crimp the edges to seal.

8. Brush the top of the pie with the egg wash.

9. Bake for 45-55 minutes, or until the crust is golden brown. Let cool for 15 minutes before slicing and serving.