unbleached all-purpose flour for work surface
1 box frozen puff pastry (Pepperidge Farm, 1.1 pound), thawed in box in refrigerator overnight
1 large egg , beaten
2 ounces grated Parmesan cheese (about 1 cup)
1 pound plum tomatoes (about 3 to 4 medium), cored and cut crosswise into 1/4-inch-thick slices
2 medium cloves garlic , minced or pressed through garlic press (about 2 teaspoons)
2 tablespoons extra-virgin olive oil
Ground black pepper
8 ounces whole-milk mozzarella cheese , shredded (2 cups)
2 tablespoons chopped fresh basil
1. Adjust oven rack to lower-middle position and heat oven to 425 degrees. Dust work surface with flour and unfold both pieces puff pastry onto work surface. Following illustrations below, form 1 large sheet with border, using beaten egg as directed. Sprinkle Parmesan evenly over shell; using fork, uniformly and thoroughly poke holes in shell. Bake 13 to 15 minutes, then reduce oven temperature to 350 degrees; continue to bake until golden brown and crisp, 13 to 15 minutes longer. Transfer to wire rack; increase oven temperature to 425 degrees.
2. While shell bakes, place tomato slices in single layer on double layer paper towels and sprinkle evenly with 1/2 teaspoon salt; let stand 30 minutes. Place second double layer paper towels on top of tomatoes and press firmly to dry tomatoes. Combine garlic, olive oil, and pinch each salt and pepper in small bowl; set aside.
3. Sprinkle mozzarella evenly over warm (or cool, if made ahead) baked shell. Shingle tomato slices widthwise on top of cheese (about 4 slices per row); brush tomatoes with garlic oil. Bake until shell is deep golden brown and cheese is melted, 15 to 17 minutes. Cool on wire rack 5 minutes, sprinkle with basil, slide onto cutting board or serving platter, cut into pieces, and serve.