Mix sugar, applesauce, egg, and vanilla extract together in a large bowl.
Combine flour, baking powder, cinnamon, and nutmeg in a separate bowl. Pour into the applesauce mixture; mix until a thick dough forms. Place dough in the refrigerator.
Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish with cooking spray.
Combine blackberries and tapioca in a saucepan over low heat; cook and stir until mixture is the consistency of a runny jam, about 10 minutes. Remove from heat.
Turn dough out onto a floured work surface; knead about 10 times. Divide dough into 2 pieces. Roll each piece to 1/4-inch thickness. Press 1 piece of rolled dough into the prepared baking dish.
Melt chocolate chips in a microwave-safe glass or ceramic bowl in 15-second intervals, stirring after each melting, 1 to 3 minutes. Spread chocolate over dough.
Spread blackberry mixture over the chocolate. Cover blackberry mixture with the second piece of dough.
Bake in the preheated oven until top is golden brown, about 30 minutes. Let cool before before slicing, at least 15 minutes.
