1 unbaked pie crust (about 10 ounces), thawed if frozen
6 ounces feta cheese (1 1/2 cups), crumbled
1 medium shallot, diced
4 sprigs of fresh thyme, plus 1 tablespoon fresh thyme leaves, divided
1 tablespoon chopped fresh basil leaves
1/2 teaspoon kosher salt
1/4 teaspoon freshly ground black pepper
3 medium tomatoes (about 1 pound total), sliced 1/4-inch thick
Arrange a rack in the middle of the oven and heat to 400°F. Line a baking sheet with parchment paper.
Place the pie crust on a lightly floured work surface. Using a rolling pin, roll the dough out to a 12-inch round that's about 1/8-inch thick. It's okay if the dough isn't perfectly round.
Starting on one end of the dough, loosely roll up the pie crust around the rolling pin. Transfer it to the prepared baking sheet and unroll the dough back out flat.
Sprinkle the cheese evenly over the dough, leaving a 2-inch border. Sprinkle with the shallot, thyme leaves, basil, salt, and pepper. Arrange the tomatoes over the cheese and herbs.
Gently fold the edges of the dough over the tomatoes, covering about 2 inches of the filling and pleating the dough every 2 inches as you go. Top with the thyme sprigs.
Bake until the crust is golden-brown and the tomatoes are soft, about 40 to 45 minutes. Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool for 10 minutes more. Serve warm or at room temperature.