Preheat your oven to 400°F (200°C). Roll out the chilled pastry on a lightly floured surface into a 12-inch circle, then transfer it to a baking sheet lined with parchment paper. Prick the crust all over with a fork to prevent puffing up during baking.
Spread a thin layer of Dijon mustard or cheese spread over the surface of the crust, leaving about a 1-inch border around the edges. This creates a flavorful base and helps prevent sogginess.
Bake the crust in the preheated oven for about 8-10 minutes, or until it just starts to turn golden and crisp around the edges. Remove from the oven and let it cool slightly.
While the crust cools, prepare the tomatoes by slicing them into thick rounds and sprinkling them with a bit of salt. Let sit for a few minutes, then blot excess juice with paper towels to minimize sogginess.
Arrange the tomato slices in a tight, circular pattern over the crust, working from the outside in. Overlap slices generously, and press them lightly into the spread layer to help them stay in place.
Sprinkle the chopped basil over the tomatoes, then drizzle with a little olive oil. Season with salt and pepper to taste, then finish with a sprinkle of grated Parmesan or feta if desired.
Place the assembled tart back into the oven and bake for an additional 10-12 minutes, until the crust is golden and crisp, and the tomato juices are bubbling gently.
Remove the tart from the oven and let it rest for a few minutes. Drizzle with a bit more olive oil if desired, then slice and serve while warm or at room temperature.
