In a large pan, melt the butter and one tablespoon of the sugar together. When it starts to caramelize, add the tomatoes, sprinkle with salt and pepper, and cook for 5 to 6 minutes. Sprinkle one tablespoon of sugar all over. Season with salt & pepper.
Add the balsamic vinegar and reduce for 2 minutes. Place the tomatoes in a tart pan. Place the pastry on top of the tomatoes and tuck the sides in. Place the tart in the oven and bake for 25 minutes, or until pastry is golden brown.
Leave the tart to rest for 5 minutes, then flip over on a plate. Pour as much excess liquid as possible. Garnish the tart with fresh thyme leaves.