1. Preheat the oven to 375°.
2. Blind-bake the piecrust first. Press the crust evenly into a 9-inch pan and prick the bottom of the crust all over with a fork. Line the crust with parchment paper and fill the pan with pie weights or dried beans. Bake until the crust begins to turn slightly golden around the edges—around 10 minutes. Remove the piecrust from the oven and set it aside to cool.
3. Once the crust is cool, slice the tomatoes evenly and arrange them in the piecrust in a single layer. Drizzle the olive oil over the top. Sprinkle the chopped fresh herbs on top of the tomatoes, then arrange the slices of cheese on top.
4. Bake the tart for 30 minutes—until the tomatoes are tender and the cheese is just starting to bubble. Let the pie cool completely. When ready to serve, season with salt, pepper, and a drizzle of balsamic vinegar.