For the crust: Place an oven rack in the center of the oven. Preheat the oven to 425 degrees F. Place the pie crust on an ungreased baking sheet and bake for 7 minutes until lightly golden. Cool for 20 minutes.
For the pesto: In a blender or food processor, pulse the basil, pine nuts, garlic, 1/2 teaspoon of salt, and 1/4 teaspoon pepper until finely chopped. With the machine running, slowly add the olive oil until the mixture forms a smooth and thick consistency. Add the Parmesan and pulse until combined. Season with salt and pepper, to taste.
Using a spatula, spread the pesto over the cooled crust. Arrange the tomato slices on top of the pesto and garnish with the sliced basil. Drizzle with olive oil and sprinkle with salt. Cut the tart into wedges and serve.
*To toast pine nuts, place on a baking sheet in a single layer and bake for 8 to 10 minutes in a preheated 350 degree F oven until lightly browned.