Preheat oven to 350°F Butter a 9-inch square baking pan with 1/2 teaspoons of the butter. Sift together the flour, cocoa, baking powder and salt.
Using an electric mixer, beat the sugar and the remaining butter. Add the egg and vanilla and beat util fluffy. Beat in the chocolate, then the applesauce. Beat in the dry ingredients on low speed until combined. Spread the batter in the prepared pan. Bake about 25 minutes, or until a tooothpick inserted in the center comes out clean. Let cool, then cut into squares.