Preheat your oven to 375°F (190°C). Lightly grease a 9-inch pie dish.

Roll out the pie crust and gently press it into the pie dish. Trim any excess dough and crimp the edges as desired.

In a large mixing bowl, combine the sliced peaches, granulated sugar, brown sugar, cornstarch, cinnamon, nutmeg, and salt. Toss until the peaches are evenly coated.

Pour the peach mixture into the prepared pie crust, spreading it out evenly.

In a separate bowl, whisk together the heavy cream and vanilla extract. Pour the cream mixture evenly over the peaches.

Brush the edges of the pie crust with the beaten egg for a golden finish.

Bake the pie in the preheated oven for 40-45 minutes, or until the filling is bubbly and the crust is golden brown.

Remove the pie from the oven and allow it to cool for at least 1 hour to set before serving.

Slice and serve the Peaches and Cream Pie as is, or with whipped cream or vanilla ice cream.