Preheat oven to 350°F. Grease a 9 x 5-inch loaf pan and line it with parchment paper, leaving an overhang in at least one direction for easy removal.
Peel and core the apples, then chop them into ¾-inch pieces.
Toss with granulated sugar, cinnamon, and nutmeg, and set aside. The apples will become slightly syrupy as the sugar draws out moisture.
In a large bowl, mix together the flour, granulated sugar, baking powder, and salt.
Create a well in the center, then add the oat milk, oil, and vanilla extract. Stir until smooth and well combined.
In a small bowl, mix together the light brown sugar, flour, and cinnamon.
Add the oil and water, then use your fingers or a fork to combine until small clumps form.