Preheat the oven to 400 degrees F.

Roll the chilled dough into a 12-inch circle on a lightly floured surface. Transfer it to a 9-inch tart pan with a removable bottom, pressing it gently into the bottom and sides. Trim away any excess dough and prick the bottom all over with a fork.

Line the crust with parchment paper and fill with pie weights or dried beans. Bake for 15 minutes, lower the oven temperature to 375 degrees, then carefully remove the parchment and weights. Return the crust to the oven and bake for 5-7 minutes, until the bottom looks dry and the edges are lightly golden. Let cool for 10 minutes.

While the crust cools, combine the goat cheese, cream cheese, extra virgin olive oil, heavy cream, ¼ teaspoon kosher salt, and ¼ teaspoon freshly ground black pepper in a stand mixer fitted with the paddle attachment (or a food processor). Beat until smooth and fluffy, scraping down the sides as needed. Add the finely chopped basil and mix until evenly incorporated.

Spread the whipped goat cheese mixture evenly over the cooled crust.

Slice the tomatoes into ¼-inch-thick slices. Arrange them in a single layer on a paper towel-lined baking sheet and sprinkle with ½ teaspoon kosher salt. Let them sit for 15-20 minutes to draw out excess moisture, then gently blot the tops with additional paper towels.

Arrange the tomato slices over the goat cheese. Top with freshly ground black pepper.

Bake at 375 degrees for 25-30 minutes, until the tomatoes have softened and the crust is golden around the edges.

Let the tart cool for at least 15 minutes before removing it from the pan. Scatter with the torn basil and serve warm or at room temperature.