In a mixing bowl, stir together flour and salt.
Add in butter and toss to coat in flour. Press the butter pieces between your thumb and side of your index finger to smush into small pieces. You want the butter pieces to vary between pea-sized and coin-sized and all coated in flour. Work quickly to keep the butter cold.
Make a well in the middle of the flour and pour in ice cold water. Mix the flour into the water until it forms a shaggy dough that is quite dry but holds together when pressed.
Turn the dough out onto a sheet of plastic wrap. Press dough together with your hands and fold it onto itself a couple of times until it comes together. Shape dough into a flattened disc, wrap with plastic wrap, and chill in the fridge for at least 1 hour or preferably overnight.
Let dough sit at room temperature for 10-15 minutes before rolling. Line a baking sheet with parchment paper and slice up your peaches and plums while you wait.
On a floured surface, roll dough out to about ⅛" thick, lifting and turning the dough occasionally so that it doesn't stick to the counter. Carefully transfer the dough onto your lined baking sheet.
Arrange your peach and plum slices in the middle of the dough, leaving a 2" border around the edges empty. In a small bowl, stir together 1 tablespoon of turbinado sugar and cinnamon. Sprinkle mixture over the filling.
Fold over the edges of the dough, overlapping where needed. Chill the assembled galette in the fridge for 10 minutes to firm up. Preheat the oven to 400°F while you wait.
Right before baking, whisk the egg and use a pastry brush to apply the egg wash to the galette dough. Sprinkle dough with a few pinches of turbinado sugar.
Bake galette for 40-45 mins or until the filling is bubbling and crust is golden brown. Serve galette while warm with a scoop of ice cream.