Beat the cream cheese, butter and granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 2 minutes, scraping down the bowl as needed. Reduce the mixer speed to low and beat in the flour and salt until combined. Divide the dough between 2 large pieces of plastic wrap. Flatten into 1/2-inch-thick disks and wrap. Refrigerate until firm, at least 1 hour or overnight.
Preheat the oven to 350˚. Line 2 baking sheets with parchment paper. Roll out 1 disk of dough on a lightly floured surface until about 1/8 inch thick, dusting with more flour as needed. Cut out 2 1/2-inch squares using a sharp knife or a 2 1/2-inch square cutter. Lift the cutouts using an offset spatula and arrange 2 inches apart on one of the prepared pans. Gather the scraps and refrigerate.
Spoon 1 teaspoon preserves onto the center of each cutout. Fold in two opposite corners to overlap in the middle and press down to seal, spreading the preserves slightly. Sprinkle the dough with coarse sugar.
Bake, rotating the pan halfway through, until the cookies are puffed and the edges are golden, 20 to 25 minutes. Let cool 5 minutes on the pan, then remove the cookies to a rack to cool completely.
Repeat with the other disk of dough, plus the reserved scraps, to make more cookies.