In a very large bowl, with a pastry cutter, cut in the shortening, salt, cottage cheese and flour. Cover and refrigerate for at least 2 hours or overnight. (Overnight is always easier for me)
Preheat oven to 400 degrees F. Line 4 cookie sheets with parchment paper.
Remove dough from bowl and place on a floured surface and shape in a log about 12 inches long. Cut into 5 equal parts. Put 4 back into the bowl and return them to the refrigerator. Roll out the remaining portion onto a well floured surface to about 15 inches in diameter (about 1/8” thick). Using a pizza wheel, cut dough into 8ths and put a slice or two of apple on the outer edge of each section. Starting at the outer edge, roll to the center. Repeat with each dough part. Place on prepared cookie sheets about 2 inches apart and bake 30 to 35 minutes.
Mix all ingredients until smooth and drizzle over the hot turnovers as they come out of the oven. Let cool 10 minutes before removing from pan.