Step 1: Make the Crust  

1. In a large bowl, combine flour and salt. Cut in chilled butter using a pastry cutter or fork until the mixture resembles coarse crumbs.

2. Gradually add ice-cold water, 1 tablespoon at a time, mixing until the dough comes together.

3. Divide the dough into two equal portions, shape them into discs, wrap in plastic wrap, and refrigerate for at least 1 hour.

Step 2: Prepare the Filling 

1. In a large bowl, combine sliced pears, granulated sugar, brown sugar, flour, cinnamon, nutmeg, lemon juice, and vanilla extract. Toss until the pears are evenly coated.

Step 3: Assemble the Pie

1. Preheat your oven to 375°F (190°C).

2. Roll out one dough disc on a floured surface to fit a 9-inch pie dish. Place it into the dish, trimming the edges if needed.

3. Pour the pear filling into the crust, spreading it evenly.

4. Roll out the second dough disc and place it over the filling. Alternatively, cut it into strips for a lattice design. Seal the edges and crimp with a fork or your fingers.

5. Brush the top crust with the beaten egg and sprinkle with sugar, if desired. Cut small slits in the top crust to allow steam to escape.

Step 4: Bake the Pie

1. Place the pie on the lower oven rack and bake for 45-55 minutes, or until the crust is golden brown and the filling is bubbling.

2. Check halfway through and cover the edges with foil if they are browning too quickly.

Step 5: Cool and Serve  

1. Allow the pie to cool for at least 1 hour to let the filling set.

2. Slice and serve with whipped cream or vanilla ice cream.