Position an oven rack in the center of the oven and preheat oven to 375 degrees F.
In a medium bowl, using a wooden spoon, mix the vegetable shortening and sugar until light and fluffy. Add the milk and vanilla and mix until smooth. Beat in the egg until incorporated.
In a separate bowl, whisk together the flour, salt, cocoa, and baking soda until smooth and combined. Gradually mix the dry ingredients into the wet mixture until fully incorporated. Do not over mix or the dough will become tough.
Form about 2 tablespoons of dough into 1 1/2-inch balls and place on ungreased cookie sheets about 2 inches apart. Press down lightly and gently round edges. Bake for about 12 minutes, rotating the pan halfway through baking.
Remove from oven and let cool completely.