Preheat the oven to 400 degrees F. Line a baking sheet with a silicone baking mat or parchment paper.
In a small bowl add 1/2 cup of sugar and the salt. Stir to combine and pour about half of it evenly onto a work surface. With your hands, press the dough into the sugar and roll out into a flat disk, about 1/2-inch thick. Sprinkle the remaining 1/2 of the sugar evenly over the top of the dough and press it a few times to adhere. With a rolling pin, roll the dough into a thickness of about 1/8-inch, turning and flipping as you roll to incorporate the sugar into the dough and to keep it from sticking to the surface. With a 3-inch round cutter, cut out 12 dough rounds and arrange them on the lined baking sheet. Transfer to the oven and bake until crisp and golden, 20 to 25 minutes. Remove from the oven and cool the crisp rounds completely on the pan.
Meanwhile, pour the balsamic vinegar into a small saucepan and bring it to a simmer over medium-high heat. Simmer until thick and syrupy, about 4 minutes; it should still swirl in the pan. If too thick, simply add about a teaspoon of balsamic, stir, and remove from the heat.
Put the strawberries in a small bowl and sprinkle them with 1 tablespoon of sugar. Let them stand until juicy, 5 to 10 minutes. To assemble the tarts, spread about 2 teaspoons mascarpone on each crisp dough round with a spoon or small offset spatula. Using a spoon to drain any excess liquid, put about 1 tablespoon of diced strawberries on the top of each tart. Drizzle a little balsamic syrup over the tarts and serve immediately.
Cook's Note: The sugared dough scraps can be tossed with cinnamon and baked in the 400 degree F oven until browned and crisp as a treat for the little ones. Leftover strawberries or balsamic syrup are delicious over ice cream!