Pour the milk over the oats in a mixing bowl and let them soak for a few minutes.
Add the egg, grated carrot, chopped green onion, salt, black pepper and shredded cheese, then mix everything well.
Line a baking sheet with parchment paper.
Spread the mixture evenly on the prepared baking sheet.
Bake at 350°F (180°C) for about 20 minutes, until the bake is set and lightly golden on top.
Allow to cool slightly, then cut into slices and serve warm or at room temperature.