On a lightly floured surface, roll out the puff pastry dough to 1/16-inch thickness. Cut out a 12-inch round, and place it on a rimmed baking sheet lined with parchment paper. Chill the dough in the freezer for at least 15 minutes or up to an hour.

Preheat the oven to 450°F.

Heat the olive oil in a 10-inch sauté pan over medium to medium-low heat. Add the leeks, 1/2 teaspoon salt, and 1/8 teaspoon white pepper. Cook, stirring as needed, until the leeks have softened, 5 to 7 minutes. Remove the pan from the heat and transfer the leeks to a plate; let them cool until you’re ready to assemble the galette.

Slice the tomatoes into 1/4-inch-thick rounds, and arrange them in one even layer on a wire rack set over a baking sheet. Sprinkle with ¼ teaspoon salt, and set aside to drain for 10 minutes.

Meanwhile, slice the zucchini into 1/8-inch-thick rounds. In a small bowl, mix the zucchini slices with 1 tablespoon of the extra-virgin olive oil, 1/4 teaspoon salt, and 1/8 teaspoon white pepper. Set aside.

In a medium-size bowl, combine the goat cheese, thyme, 1/2 teaspoon salt, 1/4 teaspoon white pepper,and 2 tablespoons of the extra-virgin olive oil. Mix well with a rubber spatula. Squeeze each head of roasted garlic over the bowl, pressing the soft cloves out of the peel. Mix until the goat cheese is smooth and the mixture is uniform.

Remove the baking sheet from the freezer (it is okay if the dough is frozen—it will soften by the time you complete the assembly) and spread the goat cheese mixture evenly over the dough, leaving a 1-inch border around the edges. Spread the sautéed leeks evenly over the goat cheese. Blot the tomatoes dry and arrange them in a concentric pattern over the leeks. Arrange the zucchini slices in a concentric pattern over the tomatoes. Sprinkle the Parmesan evenly over the top. Fold the border of the pastry up and over the edge of the tomatoes.

Bake the galette for 20 minutes, or until the crust is golden and puffed.

Remove the galette from the oven, sprinkle the fresh basil over the top, and drizzle with the remaining 2 tablespoons extra-virgin olive oil. Set the galette aside for at least 15 minutes before slicing and serving.