Rub the cold, diced butter into the flour, salt, and sugar with your fingers until it is well combined, and looks more like breadcrumbs. Mix in the ice cold water and bring the dough together into one lump. Wrap it in plastic wrap or large ziplock bag and store in the fridge for about 30 minutes.
Preheat an oven to 400F (200C). Place the pastry on a floured surface, roll out into a circle about 16-by-18-inch and 1/16 to 1/8 inch thick. Spread 1 tablespoon of peach or plum jam all around. Transfer the crust in the well greased and floured circular pie pan, or line the pan with a parchment paper. Scatter a spoon of the flour and sugar over the rolled out pastry, leaving a border of about 3-4 inches all around the edge; This will help, so your galette bottom would not become soggy during baking.
Arrange the peach and plum slices and fan around the center of the disc. I used two of each for the fan, then one plum and one peach dice into smaller cubes. Add diced peach and plum around the peach/plum fan that is in the center. Drizzle the filling with a bit of Peach Extract. Close the crust over the diced fruit and until you reach the fruit fan. Brush the edges of the pastry with melted butter or beaten egg. Add about 1 tablespoon of cubed butter or just use chunks or butter all around fruit fan and then dust it all with sugar.
Bake the Galette in the middle of the oven for about 40 to 45 minutes, until the filling is bubbling and the crust looks nicely golden brown. Allow it to cool down for a bit and enjoy it with ice cream or a dollop of whipped cream.
You may add some berries like I did, blueberry, raspberry or blackberry. Instead of Peach extract, you may add vanilla extract. Peach Extract gives you a richer flavor.