1. Preheat the oven to 325. Line cookie sheets with parchment.
2. In a large mixing bowl, cream together the shortening, butter and sugar until smooth.
3. In a liquid measuring cup, stir together the milk, vinegar and vanilla; add this to the butter mixture, beating until well combined. This mixture will look curdled, which is okay.
4. Add the nutmeg, flour, baking soda, and salt and beat until the mixture forms a cohesive dough.
5. Drop the dough by tablespoonful onto the cookie sheets. Using the bottom of a drinking glass dipped in sugar, flatten the balls to 1/4 inch thick.
6. Bake the cookies for 20 minutes, or until they're a light gold color and just beginning to brown.
7. Remove them from oven and transfer to a rack to cool. As they cool, they'll become crisp. If you want them to remain crisp, store in an airtight container when they're totally cool.