Preheat the oven to 375°F. Spray a rimmed baking tray with nonstick cooking spray. Line a large plate or baking sheet with paper towels and place the tomato slices on them. Using a second layer of paper towels, lightly blot the tops of the tomatoes. This will remove excess moisture and prevent your puff pastry from being soggy.

Lightly dust a work surface with a bit of flour to prevent your puff pastry from sticking. Using a rolling pin, roll the dough into a 12 x 12-inch square. Place the puff pastry on the baking sheet. Using the tip of a sharp knife, cut a narrow border (about ¾ of an inch) around all four edges, piercing the pastry but not cutting all the way through. Use a fork to prick the pastry all over within the borders.

In a small bowl mix the mascarpone, goat cheese, shallot, and ¼ teaspoon salt. Using an offset spatula, evenly spread the mixture on the puff pastry, leaving ½-inch border on each side.

Sprinkle the tomatoes on both sides with the remaining ¾ teaspoon salt and arrange on the pastry. Drizzle with olive oil. Bake the tart on the center rack for 30-35 minutes or until the crust is light golden brown. Turn the oven to broil (or as high as it goes) and cook 2 to 3 minutes longer until the crust is nicely browned and the filling is bubbly. Watch closely to prevent burning.

While the tart is baking, heat a small saucepan over medium-low heat and add the balsamic vinegar and sugar. Simmer the mixture for about 10 minutes or until the balsamic is slightly thickened and reduced. Garnish the tart with the balsamic vinegar, chives, and Maldon salt.