Place flour, sugar, salt, and butter in a food processor. Pulse until mixture resembles coarse crumbs. Add egg and water to the food processor, pulsing to incorporate. Pulse until dough comes together. Turn out dough onto a sheet of parchment and shape into a disk. Place another sheet of parchment on top and roll out to an 11-inch disk. Slide onto a plate or tray and freeze for 10 minutes, until firm but not so hard that it will crack when bent. Line a 9.5-inch tart pan, preferably one with a removable bottom, with the dough. Trim excess dough and prick the bottom with a fork. Freeze for 20 minutes, until solid.

Preheat the oven to 375ºF with rack in center. Place the tart pan on a rimmed baking sheet. Weigh the crust down with parchment paper and pie weights, dried beans, or rice. Bake crust for 20 minutes. Remove parchment and weights. If there are any cracks or breaks, you can patch with the remaining dough. Bake for 5 minutes more. Remove from oven and let cool.

Meanwhile, place tomato slices on a rimmed baking sheet and lightly sprinkle with salt. Combine garlic, parsley, basil, and ½ teaspoon salt in a food processor. Pulse until finely chopped. Add olive oil and pulse until a spreadable paste forms. Blot tomatoes with paper towels to remove excess liquid.

Using a small spoon or offset spatula, spread Dijon mustard evenly on the bottom of the crust. Evenly distribute cheese on top. Dollop with herb mixture and gently spread to cover in a thin layer. Top with tomatoes, overlapping. Cut smaller pieces of tomatoes to fill gaps. Lightly brush tomatoes with olive oil and sprinkle with freshly ground pepper.

Bake tart until tomatoes are softened and the crust is golden, about 50 minutes and up to 1 hour, until the tomatoes are deeply roasted. Allow to cool slightly then serve warm or at room temperature.