01 - Combine flour and salt in a large bowl. Add cold butter and cut in with a pastry blender or fingers until mixture resembles coarse crumbs. Gradually add ice water and vinegar, stirring just until dough forms. Shape into a disk, wrap in plastic, and refrigerate for at least 30 minutes.
02 - Set oven temperature to 400°F (200°C) to ensure proper roasting and baking.
03 - Toss zucchini, red bell pepper, red onion, and mushrooms with olive oil, salt, pepper, and thyme on a baking sheet. Roast for 20 minutes, stirring halfway through, until tender and lightly caramelized. Allow to cool briefly.
04 - On a lightly floured surface, roll chilled dough into a 12-inch circle. Transfer to a parchment-lined baking sheet.
05 - Arrange roasted vegetables in the center of the dough, leaving a 2-inch border around the perimeter. Sprinkle with crumbled goat cheese.
06 - Fold the dough edges over the filling, pleating as needed to encase the vegetables. Brush the crust with beaten egg to enhance browning.
07 - Bake for 25 to 30 minutes until the crust is golden brown. Let rest slightly before slicing to serve.