In a large bowl, whisk together the flour and salt. Add the cold, cubed butter and cut it into the flour using a pastry blender or your fingertips until the mixture resembles coarse crumbs.
Gradually add cold water, kneading until the dough comes together into a smooth ball. Wrap in plastic wrap and refrigerate for 30 minutes.
Meanwhile, slice the tomatoes, zucchini, and bell pepper into thin rounds. Drizzle with olive oil and sprinkle with chopped rosemary.
Preheat the oven to 400°F (200°C).
On a lightly floured surface, roll out the chilled dough into a circle about 1/8 inch (3-4 mm) thick. Transfer to a baking sheet lined with parchment paper.
Sprinkle the center of the dough with grated cheese, leaving a 1-1.5 inch (3-4 cm) border.
Arrange the tomato, zucchini, and bell pepper slices on top of the cheese. Fold the edges of the dough over the vegetables, creating a rustic shape.
Brush the edges of the dough with beaten egg for a golden-brown color during baking.
Bake the galette for 30-35 minutes, or until the crust is golden brown and crispy.
Serve warm or at room temperature, garnished with fresh herbs.
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