Preheat oven to 350°F.
Lightly grease an 8- by 8-inch baking dish with coconut oil or nonstick cooking spray.
In a medium bowl, combine applesauce and honey. Mix until smooth.
Whisk eggs in a small bowl. Add eggs and vanilla to the applesauce and honey mixture. Mix until well combined.
In a separate bowl, combine flour, cocoa powder, baking soda and salt. Mix thoroughly until smooth.
Slowly add dry mixture to wet ingredients, mixing as you go.
Pour batter into baking dish. Set aside.
Melt white chocolate chips in a double boiler. Stir in matcha powder until completely combined.
Spoon dollops of matcha white chocolate mixture into brownie batter. Swirl using a toothpick or butter knife.
Bake 25–30 minutes, or until a toothpick inserted into center of pan comes out clean.
This recipe is vegetarian and gluten-free.