Preheat the oven to 350°F (175°C) and lightly coat an 8x8 inch baking dish with non-stick cooking spray.
In a large mixing bowl, combine the rolled oats, protein powder, baking powder, cinnamon, and salt until evenly distributed.
In a separate medium bowl, whisk together the egg whites, almond milk, Greek yogurt, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Gently fold in the blueberries, raspberries, and blackberries, taking care not to crush the fruit.
Transfer the mixture into the prepared baking dish and spread evenly with a spatula.
Bake for 30 to 35 minutes, or until the center is firm to the touch and the edges are golden brown.
Remove from the oven and allow to cool for at least 10 minutes before slicing into 6 equal portions.