In a mixing bowl, combine flour and salt. Add cold cubed butter and mix until the mixture resembles coarse crumbs.

Gradually add ice water, mixing until the dough comes together. Form into a disk, wrap in plastic, and refrigerate for at least 30 minutes.

In a saucepan over medium heat, combine strawberries, peaches, granulated sugar, brown sugar, cornstarch, and vanilla extract. Cook until the mixture starts to bubble and thicken, about 5-7 minutes.

Remove from heat and stir in the cooled brown butter. Let it cool slightly.

Preheat the oven to 375°F (190°C). Roll out the chilled pie crust on a floured surface and fit it into the pie dish.

Pour the fruit filling into the crust, spreading it evenly. Roll out the remaining dough for a top crust, place it over the filling, and seal the edges.

Brush the top crust with milk and sprinkle sugar over it.

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

Let the pie cool for at least 15 minutes before serving.