Preheat your oven to 425°F.
In a large mixing bowl, combine the sliced strawberries and peaches. Add honey, lemon juice, cornstarch, vanilla extract, cinnamon, and salt. Gently toss the mixture until the fruit is well coated. Let it sit for about 10 minutes to allow the juices to develop.
Roll out the pie crust and fit it into a 9-inch pie pan. Pour the fruit mixture into the crust, making sure to distribute it evenly. Dot the top with small pieces of butter.
Cover the pie with a second crust or create a lattice top. If using a full crust, cut slits for steam to escape. Brush the top crust with the beaten egg and sprinkle with sugar.
Bake in the preheated oven for 15 minutes. Reduce the temperature to 350°F and continue baking for an additional 30-35 minutes, or until the crust is golden brown and the filling is bubbly.
Remove from the oven and let the pie cool for at least 1 hour before serving to allow the filling to set.