In a large mixing bowl, whisk flour and salt until combined. Add cold butter pieces and use a pastry blender or fingers to cut butter into flour until mixture resembles coarse sand with visible pea-sized butter clumps.
Drizzle in ice water and vinegar, mixing gently with a fork until dough begins to form. Knead 2-3 times until just combined. Shape into a disc, wrap in plastic, and chill for 1 hour.
On a floured surface, roll dough into a 12-14 inch circle (about 1/8 inch thick). Transfer to a parchment-lined baking sheet.
Top dough with tomato slices, overlapping slightly. Season heavily with salt. Brush exposed dough edges with water and sprinkle with thyme.
Spread pesto over tomatoes, leaving a 2-inch border. Top with crumbled stracciatella and lemon zest.
Fold edges of dough over filling, pleating as you go. Brush with egg wash for a golden glaze.
Bake at 400°F (200°C) for 40-50 minutes, rotating halfway, until crust is deep golden and tomatoes are caramelized. Let rest 10 minutes before serving.