Roll the chilled pie dough out on a floured work surface to a diameter of about 12 inches. Fold in half, and gently transfer to a tart pan or dish, or a pie dish. Press into the pan along the bottom and sides. Use a knife or scissors to trim away all but about ¼-inch of the dough overhang. Fold the dough back over the edge and press with fingers to cause a double-thick layer of dough along the upper edge of the pan. Place back in the refrigerator.
Place the sliced tomatoes on a baking sheet and sprinkle both sides of the slices with salt. Transfer the slices to a cutting board covered with paper towels. Let sit for 20 to 60 minutes. If paper towels become completely saturated with liquid, transfer the slices to a new set of paper towels.
Preheat oven to 375°F.
In a medium saucepan over medium heat, add the olive oil. Once shimmering add the scallions and garlic and cook until soft and aromatic, about 2 minutes. Add the corn and cook for another 1 minute. Turn off the heat and stir in the basil, thyme, ½ teaspoon salt, and ½ teaspoon black pepper. Transfer the mixture to a bowl and let cool.
Remove the tart pan with dough in it from the refrigerator and place it on a baking sheet. Add the corn/herb mixture, spreading to cover the dough. Next, sprinkle on the cheese, and finally place the sliced tomatoes over the top, overlapping some is okay. Use the halved cherry tomatoes to fill in any gaps.
Place the baking sheet with the tart in the oven and bake for 50 to 55 minutes, until the crust has just started to brown slightly on the edges. Remove from oven and allow to rest for at least 10 minutes. Garnish with additional chopped fresh basil.
If using a tart pan with a removable side and bottom, use oven mitts to lift the sides of the tart pan, allowing the side edge of the pan to fall away. Very carefully slide a metal spatula under the tart and remove the metal base below. Or, simply leave the metal base in place and slice the tart as desired. Serve warm or at room temperature.