Start by slicing the tomatoes into thick rounds, about 1/2 inch thick. Lay them out on a paper towel and gently pat them dry to remove excess moisture.

In a large, oven-safe skillet, melt the butter over medium heat. Add the sugar and stir until it dissolves and begins to caramelize, forming a golden-brown liquid. Carefully arrange the tomato slices in the skillet, slightly overlapping them in a circular pattern. Sprinkle with thyme, rosemary, salt, and pepper. Cook for about 5-7 minutes, allowing the tomatoes to soften and the sugar to caramelize further.

Roll out the puff pastry sheet on a lightly floured surface until it's large enough to cover the skillet. Place the pastry over the tomatoes, tucking the edges down around the tomatoes. Prick the pastry a few times with a fork to allow steam to escape.

Transfer the skillet to a preheated oven at 375°F (190°C). Bake for 25-30 minutes, or until the pastry is golden brown and puffed.

Remove the skillet from the oven and let it cool for a few minutes. Place a large plate over the skillet and carefully invert the tart onto the plate. The tomatoes should now be on top, glistening with caramelized goodness. Serve warm or at room temperature.