Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a bowl, combine flour and salt. Cut in the cold butter until the mixture resembles coarse crumbs.
Add ice water gradually, mixing until the dough comes together. Form into a disk, wrap in plastic, and chill for 30 minutes.
Roll out the dough on a floured surface into a 12-inch circle. Transfer to the prepared baking sheet.
Layer the tomatoes, basil, and mozzarella cheese in the center of the dough, leaving a 2-inch border.
Fold the edges of the dough over the filling, pleating as necessary. Brush the edges with the beaten egg.
Drizzle the filling with olive oil. Bake for 40 minutes or until the crust is golden and the filling is bubbly.
Let the galette cool slightly before slicing and serving.