Heat the oven to 375°F (190°C), conventional setting. Lightly grease an 8-inch square baking dish. Core and dice the apples into ½-inch pieces so they soften evenly.

Stir the rolled oats, cinnamon, baking powder, and salt in a large bowl. Break up any baking powder lumps before adding liquid.

In another bowl, whisk the eggs, milk, maple syrup, cooled melted butter, and vanilla. The butter should be warm rather than hot so it does not cook the eggs.

Pour the wet ingredients into the oat mixture, add the diced apples, and stir until evenly combined. Transfer to the baking dish and spread the apples and oats into an even layer. Bake promptly.

Bake for about 30–35 minutes, until the top is lightly golden and the center is set without a pool of liquid. Because this is an egg-containing casserole, check that the center reaches 160°F (71°C). Continue baking if needed.

Rest for 10 minutes so the oats absorb more liquid. Cut or spoon into six equal portions. Serve warm, adding milk at the table if you prefer a softer breakfast.