Preheat oven to 350° F.
Add flour and salt to a mixing bowl. Cut butter into small cubes and add to the flour. Make sure the butter is very cold, right out of the refrigerator. Next, using your thumbs and fingertips, work the butter into the flour until the butter is in pea-sized pieces.
Once the butter is incorporated into the flour, add the 3 Tablespoons ice-cold water. Use a fork to very gently mix in the water until the dough begins to hold together. Form into a ball, wrap in plastic and let rest in the fridge for 30 minutes. The secret is to incorporate the butter into the flour with as little handling as possible so as not to create gluten and a tough dough.
Meanwhile, slice and toss the persimmons in sugar (or applesauce) and cinnamon. Before rolling out the tart dough, remove a chunk, about ¼ cup in size and set aside for the topping. On a lightly floured board, roll out the rest of the dough into a 10-inch circle. Fold dough circle in half, lift carefully and place in tart pan. Gently press the dough against the sides of the scalloped edge and remove any extra dough. Arrange persimmon mixture on the dough. Take reserved ¼ cup of dough and break it into small chunks and sprinkle on top of the persimmon mixture. Sprinkle with chopped walnuts.
Bake at 350° F for 30 minutes until the fruit is soft.