Preheat the oven to 350ºF (180ºC) and lightly grease an 8-inch (20-cm) square or round baking dish with butter. Set aside.
Add the milk, applesauce, flax meal, and vanilla to a measuring cup. Whisk everything together with a fork to combine. Set aside.
Add the oats, brown sugar, cinnamon, baking powder, and salt to a large bowl. Stir to combine. Make a well in the middle of the oats and pour in the milk mixture. Stir everything together until well mixed, making sure to incorporate all of the dry ingredients into the milk.
Add the strawberries to the bowl and gently stir to combine. Pour the mixture into the prepared baking dish. Using a fork, redistribute the strawberries as needed. Place the pan in the preheated oven and bake for 28 to 30 minutes, or until the top is golden, the oatmeal is set, and the edges are starting to pull away from the pan. Transfer the pan to a wire rack and cool for 10 minutes before slicing and serving.