Heat oven to 425 degrees F. Line a baking sheet with parchment paper; set aside.
Unfold the pastry sheet on a lightly floured surface. Roll the pastry sheet into a 11-inch square and place in the center of the prepared baking sheet. Form a crust by folding over the edges about a ½ inch, then brush the edges with egg. Brush all over with the beaten egg.
Sprinkle the Parmesan cheese evenly with the dough, then poke the dough all over with a fork, making sure to go the whole way through the dough. Bake until golden brown, about 15 to 20 minutes. Transfer to a wire rack and let cool.
While the crust is baking, place the tomato slices on a triple layer of paper towels. Sprinkle salt and let sit for 30 minutes. Place second double layer paper towels on top of tomatoes and press firmly to dry tomatoes. In a small bowl, combine garlic, olive oil, and pinch each of salt and pepper; set aside.
Sprinkle mozzarella evenly over the bottom of the crust and layer the tomato slices evenly over the mozzarella. Drizzle olive oil mixture evenly over the tomatoes. Bake until the crust is deep golden brown and cheese is melted, 10 to 15 minutes.
Let cool on a wire rack for 5 minutes before sprinkling with basil. Transfer the tart to a cutting board and using a pizza cutter, slice into pieces and serve.