In a small bowl, whisk together the flour and salt. Set aside.
In a large bowl or stand mixer, beat together the softened butter and sugar until pale and fluffy (about 4 minutes). Add the vanilla extract and egg. Beat until combined. Add the flour mixture in 3 batches, beating in at low speed, just until a dough forms. Scrape down the sides of the bowl with a spatula and mix by hand a few times until all the flour is incorporated.
Divide the dough into two halves. Form each half into a disk and wrap them in plastic wrap or wax paper. Chill dough for an hour. (Dough may be made up two days in advance and kept refrigerated.)
Preheat oven to 350° (177°C) with racks set in the middle of the oven. Line baking sheets with parchment paper or silpats. Using a teaspoon measure, scoop a level teaspoon of dough and roll into a ball. Repeat two more times to make three balls. Using your palm or the flat bottom of a drinking glass, lightly press each ball to flatten to about 1 inch wide. Arrange them in a triangle on the baking sheet so the sides touch in the center of the triangle. Repeat this, spacing the cookies about 1 inch apart on the baking sheet.
Using the bottom of the wooden spoon handle or a dowel, make a deep indentation in the center of each round of dough. Smooth over any cracks. Chill the cookies on the cookie sheets in the refrigerator for 10-15 minutes to firm up again.
Once chilled, fill each cookie indentation with ⅛ teaspoon of preserves, using three different flavors for each cookie. Do not overfill. Bake in the preheated oven for 15 minutes or until very light, golden brown (the paler the cookie, the softer it will be). Cool for 5 minutes on the cookie sheet, then transfer to a wire rack to finish cooling completely. Repeat making cookies on cooled baking sheets.