Preheat oven to 350 degrees F (175 degrees C). Line cookie sheets with parchment paper.
In a medium bowl, stir together 4 cups flour, baking powder, nutmeg, salt, and sugar. Cut in the shortening until the mixture resembles coarse crumbs. Stir in baking soda, sour milk, beaten eggs, and vanilla. Stir as little as possible, and add the remaining flour as necessary to make dough thick enough to roll out.
On a lightly floured surface, roll out dough 1/4 inch thick. Cut into desired shapes with cookie cutters. Place cookies 1 inch apart on the prepared cookie sheets.
Bake for 8 to 10 minutes in preheated oven. Cool on baking sheets.