Preheat oven to 350°.

In a bowl, mix together flour, brown sugar, cocoa, baking soda, and salt. In a second bowl stir together water, applesauce, cider vinegar, oil, and vanilla extract ingredients. Pour liquid mixture over dry mixture and stir until batter is smooth.

Place paper muffin baking cups in a 12-hole muffin tin, and fill each one about half full. Bake until toothpick inserted in center of cupcake comes out clean, 18 to 20 minutes.

Remove from oven. Let sit 5 minutes, then turn out onto rack to completely cool.