In a food processor, pulse together flour, salt, and granulated sugar until well combined.
Add in the butter and pulse the mixture until it resembles coarse meal.
Pour in ice water, starting with 4 tablespoons, and pulse several times.
Drop the mixture onto a clean surface. Gather the dough into a ball and divide it into two portions.
Wrap each disk in plastic wrap and refrigerate for at least an hour.
Preheat your oven to 375 degrees. Line two large, rimmed baking sheets with parchment paper.
On a floured surface, roll out one disk of dough into a 13 by 11-inch rectangle.
Trim the edges to create a neat 12 by 10-inch rectangle, then cut the dough into eight 5 by 3-inch rectangles.
Place four of the rectangles on one baking sheet, spaced evenly apart.
Take 1.5 tablespoons of strawberry preserves and spread it evenly down the center of each rectangle.
Top each filled rectangle with another rectangle and seal the edges carefully.
Poke the top of each tart about four times with a toothpick.
Cover the tarts and place them in the freezer to chill for at least two hours.
Once baked, allow the tarts to cool on the baking sheets for several minutes.
In a mixing bowl, combine the powdered sugar, half and half, and vanilla extract to make the icing.
Spread the icing over the tops of the cooled tarts.