Step 1

Adjust oven rack to middle position and heat oven to 400 degrees. Bring vinegar, sugar, ½ teaspoon salt, and ¼ teaspoon pepper to simmer in 10-inch ovensafe skillet over medium-high heat, swirling skillet to dissolve sugar. Simmer vigorously, swirling skillet occasionally, until consistency resembles that of maple syrup, about 2 minutes. Add shallot, butter, and 2 teaspoons thyme and whisk until butter is fully incorporated, about 1 minute.

Step 2

Remove skillet from heat; add tomatoes and toss to coat lightly with syrup. Arrange tomatoes cut side up in as close to single layer as possible (some overlap is OK; tomatoes will shrink as they cook) and sprinkle with remaining ¼ teaspoon salt and remaining ¼ teaspoon pepper. Transfer skillet to oven and cook until liquid has evaporated and tomatoes are very lightly browned around edges and softened but not fully collapsed, about 1 hour. While tomatoes cook, prepare pastry.

Step 3

Roll pastry into 10-inch square on lightly floured counter. Using plate, bowl, or pot lid as template, cut out 10-inch round. Discard trimming. Transfer pastry round to large plate and refrigerate until needed. Remove skillet from oven and place pastry round over tomatoes. Bake until pastry is puffed, crisp, and deep golden brown, about 30 minutes, rotating skillet halfway through baking.

Step 4

Let tart cool for 8 minutes. Run paring knife around edge of crust to loosen, then invert plate over skillet. Using pot holders, swiftly and carefully invert tart onto plate (if tomatoes shift or stick to skillet, arrange with spoon). Let cool for 10 minutes, then sprinkle with remaining ½ teaspoon thyme. Serve warm or at room temperature.