Make filling: In a saucepan combine dates, 1/2 cup of the brown sugar, and water; simmer about 8 minutes, or until mixture thickens, stirring constantly.
Remove from heat and cool.
Cream shortening and the remaining sugar until light, then beat in eggs and vanilla.
Sift flour, measure, and sift again with the soda, cream of tartar, and salt.
Stir flour mixture into shortening mixture gradually to make a stiff dough.
Divide in half.
Roll out each portion on a lightly floured board, making a rectangle about 8 by 10 inches and 1/4-inch thick.
Spread with half the cooled date filling, then roll up like a jelly roll.
Wrap in waxed paper and chill thoroughly, preferably 12 hours or overnight.
Cut slices 1/4-inch thick with a sharp knife; place on an ungreased baking sheet.
Bake in 400° oven for 8 to 10 minutes.