For filling, in a medium saucepan combine dates, water, and the 1/3 cup granulated sugar. Bring to boiling; reduce heat. Cook and stir about 2 minutes or until thickened. Stir in lemon juice and the 1/2 teaspoon vanilla; cool.

In a large bowl combine butter and shortening. Beat with an electric mixer on medium to high speed for 30 seconds. Add the 1/2 cup granulated sugar, brown sugar, baking soda, and salt. Beat until combined, scraping side of bowl occasionally. Beat in egg, milk, and the 1 teaspoon vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Divide dough in half. Cover and chill about 1 hour or until dough is easy to handle.

Roll half of the dough at a time between pieces of waxed paper into a 12x10-inch rectangle. Spread with half of the filling to within 1/2 of the edges; roll up dough into a spiral. Moisten edges; pinch to seal. Wrap in plastic wrap or waxed paper. Freeze for 2 to 24 hours.

Preheat oven to 375 degrees F. Grease a large cookie sheet; set aside. Using a serrated knife, cut rolls into 1/4-inch slices. Place slices 1 inch apart on prepared cookie sheet.

Bake in preheated oven for 8 to 10 minutes or until edges are lightly browned. Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack; cool. Makes about 64 cookies.

Place in layers separated by waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.