Puff Pastry Tomato Tart with Stracciatella

Name: Puff Pastry Tomato Tart with Stracciatella
Prep time: 15 min
Cook time: 23 min
Total time: 38 min
Cuisine: American, Italian
Ingredients: 1 large ripe tomato; ½ tsp kosher salt, divided, plus more to taste; 1 sheet frozen puff pastry, thawed (from a 2-sheet package*) (*I used Pepperidge Farm); 2 tbsp grated Parmesan cheese; 1 large egg; 1 tsp water; 1 tbsp fresh thyme leaves; 1 tbsp extra-virgin olive oil (plus more for drizzling); freshly ground black pepper, to taste (to taste); 4 ounces stracciatella, or burrata filling* (see post for details); chopped fresh basil, for serving, optional