Preheat oven to 350 degrees. In a large bowl with an electric mixer, cream together soft butter and powdered sugar until fluffy and smooth. Beat in the egg yolk (save white for later in a small bowl) Mix in flour and salt until well combined. Roll the dough into a giant ball and wrap in plastic wrap. Refrigerate for 30 minutes, until dough is stiff.
Divide dough into 3 equal-sized portions. Using your hands, roll dough into 3 logs, about 12 inches long. Place logs on an ungreased cookie sheet, then pat dough down with your hands until it is about 3/4 to 1 inch thick. Using your thumb or 2 fingers, press an indent down the middle of each log, creating a section to hold the fruit filling, leaving a border at each end. Be sure not to press too far and make a hole in the dough.
In a small bowl, whisk egg white with a tsp of water, then brush mixture on top of each of the 3 logs. Empty the fruit preserves into a microwave safe bowl, and heat for 20-30 seconds until softened. Spoon into the indent in each of the logs, careful not to over-fill them so the preserves don't run out and burn on the cookie sheet. Sprinkle with chopped nuts.
Bake at 350 for 20 minutes. Remove from the oven and let cool completely on the cookie sheet. Cut the logs diagonally into 3/4-inch wide strips. Makes lots. Enjoy!