Preheat the oven to 425°. In a large bowl, toss the apples with the sugar, lemon juice, cinnamon, nutmeg and salt.
Line a 9-inch pie dish with one of the crusts, pressing firmly around all sides and smoothing out any cracks.
Add the butter to a medium-size saucepan set over medium-low heat. Do not leave your stovetop perch. Watch as the butter melts, then foams, then begins to brown, swirling occasionally as you go. The whole process should take about 4 minutes, but it’s really an eyeball (and an aromatic) thing: As soon as the butter starts to turn brown and smell nutty, remove the pan from the heat so the butter doesn’t burn. Toss the brown butter with the apples, then add the entire mixture to the pie dish. Top with the second crust, cinching the perimeter of the dough with a fork or your fingers to seal.
Using a sharp knife, cut 5 or 6 air slits into the top of the crust, and brush the crust with the egg wash.
Bake at 425° for 15 minutes. Then reduce the heat to 350° and bake for 30 more minutes, or until the crust is golden brown and the filling is bubbly. Serve with vanilla or cinnamon ice cream.