Allow the puff pastry to warm on the countertop for about 45 minutes or in the fridge for 2 hours until it is still cool, yet pliable. Preheat the oven to 400°F (204°C).
Prep the Tomatoes
Wash and slice the tomatoes, then place them in a colander with a generous sprinkle of salt. Allow them to drain while you make the tofu ricotta.
Make the Tofu Ricotta
Drain and press a container of extra-firm tofu, removing as much liquid as possible, then crumble it into a large food processor.
Add salt, garlic, nutritional yeast, olive oil, and basil. Blend well for 2 minutes in a food processor. Add a splash of soy milk if needed to thin out the ricotta to a smooth spreadable texture.
Prep the tart
On a lightly floured surface, roll out one puff pastry sheet so that it thins out and expands to approximately 3 inches longer and an inch wider than the original sheet. Use a pastry cutter or paring knife to score a ¾-inch border around the sides of the dough, without cutting all the way through. Use a fork to prick the puff pastry dough inside the border; this will prevent it from rising in that section.
Spread the vegan ricotta about 1/4 inch thick in the center of the rectangle and sprinkle with chopped fresh basil.
Use a paper towel to dab the tomato slices, removing any remaining salt and tomato juice. Then lay the tomato slices on the ricotta, slightly overlapping the slices. (Use alternating sizes and colors to add more texture and color to your tart.)
Add a dash of turmeric to 1 tbsp of plant milk, then use it to brush the edges of the puff pastry.
Bake the tomato tart at 400°F for 20-25 minutes, until the edges are puffy and golden brown. Remove it from the oven and brush it with a bit of olive oil. If the tomatoes appear dry, sprinkle with additional fresh, chopped basil, and slice for serving.
Notes
Use fresh garden tomatoes. The better the tomatoes, the better the flavor.
Cut the tomatoes by laying them on their sides. If you cut from the top down, you will have some slices with large areas of seeds.
Keep the pastry puff dough as cold as possible, yet still pliable and rollable. If the oven is still preheating after you have prepped the tart, place it in the freezer until the oven is hot.