Make the dough in advance so that it has time to chill before rolling out.
Preheat the oven to 350°F (180°C) and set a large baking sheet to the side.
Add the peaches, flour, sugar, and cinnamon to a large mixing bowl and mix until the fruit is well coated.
Lay out a large square of parchment paper and, using a rolling pin, roll the chilled dough into a round shape, about ¼-inch (5-mm) thick. Lift the rolled dough, using the parchment paper as handles, onto the baking sheet before adding the filling.
Place the fruit filling in the middle of the pastry. Use your hands to arrange the fruit evenly, leaving a 1-inch to 1.5-inch (2.5-cm to 4-cm) exposed border of crust around the edges. Fold the edges of the dough up and over the edges of the fruit.
Brush the exposed edges of pastry with beaten egg and sprinkle with coarse sugar if using.
Bake the galette for about 45 minutes, or until the crust is golden and the fruit is bubbling. Cool the galette on the baking sheet for 30 minutes before slicing and serving drizzled with cream or topped with ice cream.