1. Preheat oven to 375°F. Brush a rimmed baking sheet with olive oil. Unroll phyllo sheets and cover with a clean kitchen towel. Place a sheet of phyllo on baking sheet and lightly brush entire surface with olive oil. (It won't matter if phyllo tears slightly.) Top with a second sheet of phyllo, keeping remaining sheets covered, and brush with olive oil. Repeat stacking and brushing until all phyllo has been used. Reserve any extra oil.
2. Arrange tomato slices decoratively on phyllo in a single layer, leaving a 1/4-inch border on all sides. Sprinkle feta over the top, then sprinkle with thyme and rosemary and season with salt and pepper. Drizzle any remaining olive oil over top.
3. Bake tart until edges are golden brown and phyllo is crisp, about 30 minutes. Let tart cool in pan on a wire rack for 5 minutes. Transfer to a cutting board, cut into 12 squares and serve warm.