Roasted-Tomato Tart

Put oven racks in middle and lower third of oven and preheat oven to 400°F. Line a large shallow baking pan with foil.
Roll out pastry sheet on a lightly floured surface with a lightly floured rolling pin into an 11-inch square (1/8 inch thick). Using a plate or pot lid as a guide, cut out a 10-inch round.
Carefully transfer round to an ungreased baking sheet by rolling pastry around rolling pin and then unrolling onto baking sheet. Chill round on baking sheet until ready to use.
Toss tomatoes with 2 tablespoons oil, 2 teaspoons thyme, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a bowl until well coated. Roast tomatoes, cut sides up and in 1 layer, in foil-lined baking pan in middle of oven, 1 hour.
Brush pastry round with 2 teaspoons oil, then sprinkle with 1 teaspoon thyme. After roasting tomatoes 1 hour, move tomatoes in pan to lower third of oven and put pastry on baking sheet on middle rack. Bake pastry and tomatoes until pastry is golden brown and edges of tomatoes are slightly browned but still appear juicy, about 15 minutes.
While pastry is still warm, scatter 1/2 cup cheese shavings evenly over it. Top shavings with warm tomatoes, cut sides down and in 1 layer, then sprinkle evenly with remaining 1/2 teaspoon thyme, 1/4 teaspoon salt, pepper to taste, and additional cheese shavings if desired.