Pre-heat the oven to 425°F.

Roll the puff pastry out into a 10x14-inch rectangle and place it on a baking sheet. (Rolling the pastry out on parchment makes it very easy to transfer to the baking sheet.) Use a paring knife to score a ¾-inch border inside the perimeter of the pastry. Be careful not to cut all the way through the pastry. With the tines of a fork, make indentations around the edge to form a crust and dock the pastry by pricking it all over. Brush the perimeter of the pastry with olive oil.

Combine the mayonnaise, Parmesan cheese and oregano in a small bowl. Spread the mixture on the inside of the puff pastry in an even layer.

Arrange the slices of tomato over the mayonnaise mixture, letting the slices overlap slightly. Sprinkle the sliced shallots over the tomatoes and generously drizzle olive oil over the tomatoes. Season with freshly ground black pepper.

Transfer the baking sheet to the oven and bake for 20 to 25 minutes, or until the crust is nicely browned and the pastry has browned on the bottom.

Remove the sheet from the oven and let the tart rest for at least 10 minutes. Tear up the basil leaves and sprinkle the basil and sea salt on the tart. Cut the tart into squares or rectangles and serve warm.