1. Position an oven rack in the center of the oven and preheat the oven to 375°F. Line a baking sheet with parchment paper.

2. Core and slice the tomatoes into 1/8- to ¼-inch-thick rounds, discarding the end slices. (The tomatoes should be cut on the thin side so their juices can evaporate during baking before they have a chance to make the crust soggy.) Place the tomato rounds on paper towels. Cover with another layer of paper towels and let stand to drain excess juices while preparing the phyllo crust.

3. Place a phyllo sheet on the baking sheet. Brush the phyllo with olive oil. Top with the remaining phyllo sheets, brushing each with oil. Fold over the four sides of the phyllo stack to make a 1-inch-wide border. Sprinkle the area inside the border with the Parmesan. Top with the tomato slices, overlapping the slices as needed. Sprinkle with the goat cheese and season with salt and pepper to taste.

4. Bake until the phyllo is crisp and deep golden brown, about 20 minutes. Cool slightly or to room temperature. Sprinkle with the herbs, cut into rectangles, and serve.