Preheat the oven to 350 degrees F (175 degrees C). Line a cupcake pan with paper liners, or grease and flour cups.
In a large bowl, mix together the brown sugar, shortening and peanut butter until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Combine the flour, cream of tartar, baking soda and salt; stir into the batter alternately with the milk. Spoon into the prepared muffin cups.
Bake for 15 to 20 minutes in the preheated oven, until the top of the cupcakes spring back when lightly pressed. Cool in the pan for at least 10 minutes before removing to a wire rack to cool completely.