Cream the shortening and sugar in a large bowl with an electric mixer. Add the vanilla, and egg yolk and mix well.
Sift the flour into a separate bowl with the baking powder and salt. Add the flour mixture and milk alternately to the shortening mixture, beginning and ending with the flour mixture, and mix to form a dough. Divide the dough into 2 halves. To one half, add the chocolate, mixing thoroughly. Wrap both sections of dough in separate pieces of plastic wrap and chill in the refrigerator for about 1 hour.
Unwrap and roll each half of dough between 2 pieces of waxed paper. Roll to a 1/8-inch thickness. Remove the waxed paper from the top of each layer of dough. Place the white layer on top of the chocolate layer and roll up carefully as you would a jellyroll, using the waxed paper to roll smoothly. Wrap the roll with the waxed paper and chill overnight in the refrigerator.
The next day, preheat the oven to 375 degrees F.
Cut the roll into 1/4-inch slices (see Cook's Note) and place about 1/2 inch apart on ungreased baking sheets. Bake for about 12 minutes. Do not brown. Remove carefully with a pancake turner and cool on racks.
When cutting the roll, use a very sharp knife and wipe the blade after each slice to avoid mixing the colors and to keep the cookies round. You could also use an electric knife. To cut the dough with a thread, slide a 12-inch length under the roll, cross it over at the top and pull right through.
Adapted from "Home Cooking with Trisha Yearwood" by Trisha Yearwood © Clarkson Potter 2010. Provided courtesy of Trisha Yearwood. All rights reserved.