Someone else who calls them half-moons!! Oh, you're from NY too. Where? I grew up east of Syracuse. Everywhere else they call them Black & Whites. How boring. Here is my mom's recipe, that I believe came from her mother. hope it's close to yours:
1 1/2 c. sugar
1 c. shortening
2 eggs
3 1/2 c. flour
1 tsp. baking powder
1 tsp. baking soda
1 tsp. salt
1 1/2 tsp. vanilla
1 c. sour milk (if mom had no sour milk, she replaced a tablespoon of milk with a tablespoon of cider vinegar or lemon juice and let it sit for about 15 minutes)
Cream shortening & sugar, beat in eggs. Sift dry ingredients, and stir in with vanilla & milk. Bake on grease sheets 12 minutes at 400º.
There ya go Wish you could send me one!