Beat shortening, white sugar, and brown sugar in a bowl using an electric mixer until creamy and smooth.
Mix milk and vinegar together and let stand 5 minutes to make 'sour milk'. Stir sour milk, eggs, and vanilla extract into shortening mixture.
Sift flour, baking powder, baking soda, salt, and nutmeg together in a large bowl. Mix flour mixture into shortening mixture until incorporated. Refrigerate until fully chilled, 2 hours to overnight.
Preheat oven to 350 degrees F (175 degrees C).
Roll dough to a 1/8-inch thickness on a floured surface; cut into 2-inch rounds using a cookie cutter. Spoon 1 teaspoon preserves into the center of half the cookies; cover with remaining cookies. Lightly press edges of cookies together using a fork. Cut criss-cross slits into the top of each cookie using a knife. Arrange cookies on an ungreased baking sheet.
Bake in the preheated oven until cookies are golden, 13 to 15 minutes.