Make the filling. Mix the peaches and strawberries together in a medium bowl. Add the sugar and vanilla; toss well to coat the fruit. Set aside and allow the mixture to soak.
Make the Crust. In a medium bowl, whisk together the flour, sugar, and salt. Using a pastry cutter (or your hands), cut in the butter until the mixture resembles coarse, pea-sized crumbs. Add 1/4 cup of the ice water, stirring with a fork until the flour is moistened. Add in 2 more tablespoons of ice water if the dough seems dry. Gently knead until it all comes together. Shape the dough into a ball and flatten into a thick disk. Wrap in plastic wrap and refrigerate for 1 hour.
Preheat the oven to 220°C (425°F).
Line a large baking sheet with parchment paper or a silicone baking mat. Set aside.
On a lightly-floured surface, roll the dough into a 12-inch circle. Trim if desired and transfer to the prepared baking sheet.
Spoon the fruit (not the juices) into the centre of the dough, leaving a 2 to 3-inch border all around. Gently fold the edges of the dough, overlapping as necessary. Press gently to seal. Pour some of the reserved juices over the fruit.
Brush the crust with the beaten egg and sprinkle with sugar. Bake the tart using the convectional heat function for 35 to 45 minutes or until the crust is golden brown. Remove from the oven and cool slightly before serving.
