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