Place unsweetened chocolate and butter in a heavy saucepan over low heat, stir until chocolate melts.
Combine sugar, applesauce, eggs, and vanilla in a large bowl, mix well.
Combine flour, baking powder, soda, and salt; add to applesauce mixture, stirring well.
Stir in chocolate mixture.
Spoon the batter into a greased 9-inch square baking pan.
Bake at 350°F for 30 minutes.
Cut into squares and serve.