Sift together flour and salt onto a piece of parchment paper.
In a mixing bowl with a handheld beater or in a stand mixer with a paddle attachment, cream together thick yogurt and butter until fluffy. Add flour in several additions by holding up the parchment paper to funnel it into the mixing bowl, beating until fully incorporated after each addition.
Bring the dough together in a ball with your hands. The dough should be soft but not sticky.
Divide dough into 4 parts and flatten to 3/4" thick discs. Wrap each disc and refrigerate for at least 2 hours.
Preheat oven to 325˚F. Line two baking sheets with parchment paper.
Sprinkle 2 tablespoons of the sugar onto a clean work surface. Working with 1 disc of dough at a time, roll the dough out over the sugar to a square of about 1/16-1/8" thickness. Cut into 16 smaller squares (about 2" squares) using a fluted pastry cutter.
Spoon 1 teaspoon of preserves into the middle of each square. Fold opposite corners to meet in the middle and press firmly to seal, leaving the other two corners open. Preserves will push out from the center as you push down on the pastry.
Carefully transfer cookies to the parchment-lined baking sheets (an offset spatula works well for this), leaving about 1" of space between each cookie.
Repeat the process with the remaining discs of dough and sugar. Save the scraps of dough and re-roll them to form more cookies.
Sprinkle centers of each cookie with more sugar.
Bake at 325˚F for about 12-15 minutes until bottoms and edges are golden brown.
Transfer cookies to cooling racks and cool to room temperature. Enjoy!