1. In the bowl of an electric mixer, beat the butter on medium speed until soft and smooth. Add the sugar, vanilla, and salt and beat on medium until well blended (about 3 minutes).
2. Add egg and beat for another minute. Add flour and beat on medium speed until just blended.
3. Place 2 large pieces of plastic wrap on a work surface. Divide dough in half and place the two piece of dough on the 2 pieces of plastic and cover. Shape each one into an even flat disc. Refrigerate for about 1 hour, or until firm enough to roll out.
4. Working with one disc at a time, on a well-floured piece of parchment paper, roll the dough into a rectangle approximately 11 1/4 x 15 inches. (If yours measures a bit smaller, that is ok (but do try to keep the shape a rectangle). Don't roll the dough too thin (about 1/8 inch thick is perfect).
5. Transfer dough on parchment onto a baking sheet and refrigerate for about 1 hour.
6. Preheat oven to 350 degrees F. Line 2 baking sheets with parchment paper (or silpat liners).
7. Working with one sheet at a time, slide dough onto your work surface. Dust dough lightly with flour. Cut dough lengthwise into equal width strips (use a ruler to measure if you like). Spoon jam down the length of each strip (keep it about an inch away from the edges), then carefully fold the dough over the filling. Use your fingertips to gently seal the edges together. Roll the dough over so the seam is on the bottom. Cut the cookies into 1 1/2-inch wide pieces and arrange them about an inch apart on parchment or silpat-lined baking sheets.
8. Bake the cookies for about 15 minutes, or until the edges and bottoms are starting to brown. Transfer to wire rack to let cool completely.