Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9x12-inch baking pan.
Mix pastry flour, white sugar, brown sugar, cocoa powder, baking powder, baking soda, and salt together in a bowl. Stir bananas and peanut butter together in a separate bowl until smooth; add almond milk and oil and mix well. Carefully fold banana mixture into flour mixture until batter is just combined; fold in chocolate chips. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 40 to 45 minutes.