Combine all-purpose, self-rising flour, and salt in a large bowl; cut in butter until mixture resembles coarse crumbs. Make a well in the center of the mixture; pour in 1 beaten egg and water and bind the ingredients together gently. Do not knead too much. Shape dough into a ball, wrap in plastic and refrigerate for 4 hours or overnight.

Combine pineapple and sugar in a saucepan over medium heat; bring to a boil. Reduce heat and simmer, stirring frequently, for 30 minutes, or until mixture thickens. Remove from heat and allow to cool.

Preheat the oven to 400 degrees F (200 degrees C).

On a lightly floured surface, roll the dough out to 1/4 inch in thickness. Cut 24 rounds, using a 2 inch round fluted cutter. Place on cookie sheet. Put a spoonful of pineapple jam in the center of each piece. Decorate with criss-cross strips of pastry over jam, extending slightly onto pastry shell.

Cut 24 more 2 inch rounds, then, using a smaller cutter, cut out the centers, creating a ring shape. Moisten the edges of each pastry, and place the rings on top of each pastry shell. Brush the top of the pastry with beaten egg.