Arrange all tomatoes in a single layer on paper towels. Sprinkle with salt. Let stand for 30 minutes. Pat dry.
In the work bowl of a food processor, combine basil, pecans, cheese, garlic, and red pepper; pulse until finely chopped, stopping to scrape sides of bowl. With processor running, add ¼ cup oil in a slow, steady stream until mixture is smooth but still has texture. Transfer to an airtight container, and refrigerate for 1 hour or until ready to use.
Preheat oven to 400°. Line a large rimmed baking sheet with parchment paper.
Unfold both puff pastry sheets on prepared pan. Pinch the 2 pieces together. Trim 3½ inches from length of puff pastry to create a 15½×9¾-inch rectangle. Spread pesto in an even layer onto puff pastry, leaving a ¼-inch border around edges. Arrange heirloom tomato slices in a single layer on top of pesto. Sprinkle with cherry tomatoes. Drizzle with remaining 1½ teaspoons oil.
Bake until pastry is puffed and golden brown, 20 to 25 minutes. Let cool for 10 minutes. Garnish with cheese and basil, if desired.
Notes
*We used Cane River Pecan Company pecans.
Recipe by Louisiana Cookin' at https://louisianacookin.com/tomato-and-garden-pesto-tart/