For the Brown Butter Pie Crust:

1. Brown the Butter:

   • In a saucepan, melt the butter over medium heat. Continue to cook, swirling the pan occasionally, until the butter turns a golden-brown color and releases a nutty aroma. Be careful not to burn it. Once browned, remove from heat and let it cool to room temperature.

2. Make the Dough:

   • In a large mixing bowl, combine the flour and salt. Add the cooled brown butter and stir until it forms a crumbly mixture.

   • Gradually add the water and vinegar, stirring just until the dough begins to come together. It may look a little crumbly, but it should hold together when pressed.

3. Chill the Dough:

   • Divide the dough in half, shape each half into a disc, wrap in plastic wrap, and refrigerate for at least 1 hour. This allows the dough to firm up and makes it easier to roll out.

For the Strawberry and Peach Filling:

4. Prepare the Filling:

   • In a large mixing bowl, combine the fresh sliced peaches and quartered strawberries.

   • Add the granulated sugar, cornstarch, lemon juice, lemon zest, and fine sea salt. Toss everything together until the fruit is evenly coated and the cornstarch is well incorporated.

Assemble the Pie:

5. Roll Out the Dough:

   • Preheat the oven to 375°F (190°C).

   • Roll out one of the dough discs on a lightly floured surface into a circle large enough to fit a 9-inch pie pan. Transfer the dough to the pie pan, pressing gently into the edges.

6. Add the Filling:

   • Pour the prepared strawberry and peach filling into the pie crust.

7. Top the Pie:

   • Roll out the second disc of dough and place it over the filling, either as a full top crust or cut into strips to create a lattice pattern. If using a full crust, make a few small slits to allow steam to escape during baking.

   • Brush the top crust with the whisked egg for a golden finish and sprinkle with Turbinado sugar if desired.

8. Bake the Pie:

   • Bake the pie in the preheated oven for 45-50 minutes or until the crust is golden brown and the filling is bubbly.

   • If the edges of the crust start to brown too quickly, cover them with aluminum foil to prevent burning.

9. Cool and Serve:

   • Let the pie cool for at least 2 hours to allow the filling to set. Serve warm or at room temperature with a scoop of vanilla ice cream or whipped cream, if desired.