Preheat the oven to 400°F. Get out a large, preferably rimless, baking sheet.
On a large sheet of floured parchment paper or wax paper, roll the dough into a large rectangle slightly less than 1/4-inch thick. If you’re using parchment paper, slide the paper and pastry onto the baking sheet and trim the paper so it fits the pan. If you’re using wax paper, invert the pastry onto the pan and peel off the paper.
Spread the pesto on the pastry, leaving a 1-inch border.
In a small bowl, mix 1⁄4 cup of the Parmesan cheese and the cornmeal. Sprinkle over the pesto. Layer on tomato slices (about five slices per row). Salt and pepper, to taste. Fold the edge of the pastry over the perimeter of the tomatoes.
Bake on the center oven rack for 20 minutes. Remove from the oven, sprinkle with the remaining Parmesan cheese, and drizzle with cream. Reduce the heat to 375°F and bake for 25 to 30 minutes more, or until the crust is golden and the filling is bubbling.
Transfer to a cooling rack for 5 to 10 minutes before serving. Garnish with basil leaves.