Make The Filling: In a medium bowl, combine sliced peaches, blueberries, brown sugar, cornstarch, lemon juice, ground cinnamon and ground cardamom and toss with a wooden spoon or a rubber spatula. Set aside.
Make Pie Crust: Combine flour, salt, butter and sugar in a food processor and pulse for a few seconds until barely combined, mixture becomes crumbly and resembles coarse meal. Gradually mix in cold water and pulse a few times to combine, until the dough starts clumping together, then stop mixing. The dough at this time should be quite crumbly but still can hold together when you pinch it with your fingers. Do not process to the point that a large ball of dough is formed.
Transfer the dough to a floured surface and form into a ball. Use your hand to flatten slightly to form a 1-inch thick disc. Cover the disc with plastic wrap and refrigerate for at least 1 hour. Soften slightly at room temperature before rolling out.
Place a disc of dough in between sheets of parchment paper. Use a rolling pin dusted with flour, rolling outwards from the center of the dough with an even pressure to make a large circle, around 10-12 inch in diameter (1/8-inch thick). Remove the top sheet of parchment, then transfer the dough to a baking sheet lined with parchment paper.
Preheat oven to 350°F/175°C. Arrange sliced peaches like a big circle onto the crust, then place all blueberries into the middle of the circle; or you can arrange the fruit in a way you prefer. Make sure to leave about a 2-inch edge uncovered with fruits. Fold the edges over the filling and press slightly to seal them together.
Stir the egg in a small bowl with a fork to create an egg wash. Use a soft pastry brush to lightly coat the folds of the dough, then sprinkle with coarse sugar.
Bake the galette for 35-40 minutes or until the crust is golden brown and the fruit is bubbling. Remove the galette from the oven and let it cool before slicing.
Slice and serve with whipped cream or vanilla ice cream if desired.