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