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, vegetable oil, applesauce, and peanut butter until light and fluffy.

Beat in the eggs one at a time, then stir in the vanilla extract. Combine the flour, cream of tartar, baking soda, and salt. Stir this dry mixture into the batter alternately with the milk, beginning and ending with the dry ingredients.

Spoon the batter into the prepared muffin cups, filling them about two-thirds full (these cupcakes do not rise excessively).

Bake for 15 to 20 minutes, or until a wooden skewer inserted into the center of a cupcake comes out clean. Let the cupcakes cool in the pan for at least 10 minutes before transferring them to a wire rack to cool completely. Frost once completely cool.