Bring oats and water to a boil in a saucepan. Reduce to low and simmer for 15 minutes, stirring occasionally, until the water is mostly absorbed; remove from heat and cool for 10 minutes.
Heat oven to 350°F and butter an 8-inch square baking dish. Whisk the cup of milk with eggs, almond butter, brown sugar, cinnamon, vanilla and salt.
Stir grated apple and the warm, not hot, oats into the milk mixture. Spread evenly in the dish and bake for 35 to 40 minutes until set and at least 160°F in the center.
Rest for 15 minutes, cut into six squares and transfer to shallow containers. Refrigerate within 2 hours, chill fully, wrap portions separately and freeze for up to 2 months.
Reheat a frozen square in a microwave-safe bowl with its measured milk under a loose microwave-safe cover at 50 percent power for 2 minutes. Continue at full power in 30-second bursts until the center reaches 165°F, usually another 1 to 2 minutes, then rest for 1 minute.