Preheat your oven to 350°F. In a bowl, mix the flour and sugar. Add the butter and work it in with your fingers until you get a crumbly texture. Add the ice water, 1 tbsp at a time, until the dough comes together. Wrap it in plastic wrap and chill for 30 minutes.
In another bowl, toss the strawberries with sugar, cornstarch, and lemon juice.
Roll out the dough into a rough 12-inch circle and place it on a parchment-lined baking sheet. Spoon the strawberry mixture over the dough, leaving a border. Use the parchment paper to help fold the edges of the dough up over the fruit, creating pleats. Press gently to hold the shape. Brush the edges with the beaten egg and sprinkle the galette with a little extra sugar.
Bake for 35–40 minutes, or until the strawberries are tender, the juices are bubbling, and the crust is golden brown. Let it cool before serving.
