Preheat the oven to 350°F butter or lightly grease an 8x8 or 9x9-inch baking dish.
In a large bowl, stir together the rolled oats, cinnamon, baking powder and kosher salt.
In a separate bowl, whisk the eggs. Add the milk, applesauce, maple syrup, melted butter and vanilla and whisk until everything is well combined.
Peel and dice the apples into small pieces. Give them a light squeeze of fresh lemon juice and toss to coat.
Pour the wet ingredients into the oat mixture and stir until combined. Fold in the diced apples.
Pour everything into your prepared baking dish and spread it evenly.
For the crisp topping, add the flour, oats, brown sugar, cinnamon and salt to a food processor. Add the cold butter and pulse just until the mixture becomes crumbly. You still want to see some pieces of oats and small buttery crumbs.
Scatter the crisp mixture evenly over the oatmeal.
Bake for approximately 40–45 minutes, or until the center is set, the apples are tender and the topping is golden.
Let the baked oatmeal rest for at least 15 minutes before cutting it into squares. That little rest is what gives you the soft-but-sliceable texture rather than a scoop of loose oatmeal.