Preheat oven to 425 degrees F (220 degrees C). Line baking sheets with parchment paper.
Unroll the pie crusts, place on a lightly floured work surface, and roll the crusts slightly with a rolling pin to square the edges. Cut each crust into 8 equal-sized rectangles. Place about 2 teaspoons of strawberry jam in the center of 8 squares, and spread the jam out to within 1/4 inch of the edge of the pastry square. Top each with another pastry square, and use a fork to crimp the squares together, sealing in the jam. Use a knife to trim the pastries, if desired. Move the filled pastries to the prepared baking sheets.
Bake in the preheated oven until the edges are lightly golden brown, about 7 minutes. Allow to cool on the baking sheets. Meanwhile, stir together the confectioners' sugar, milk, and vanilla extract in a bowl to make a spreadable frosting. Spread the cooled tarts with frosting and sprinkle with colored sugar.
