Heat oven to 350°F. Line a 9×13-inch pan with parchment, leaving overhang.
Whisk flour, oats, crust sugars, 1 tsp cinnamon, and 1/2 tsp salt in a bowl.
Pour in melted butter and stir until moist crumbs form. Press about three-quarters into the pan. Reserve the rest for topping.
Bake crust 12 minutes until set at the edges. Cool 5 minutes.
Toss apples with lemon juice, filling sugars, 1 1/2 tsp cinnamon, nutmeg, and 1/4 tsp salt. Stir in vanilla, then sprinkle in cornstarch and mix again.
Spread apple mixture over warm crust. Crumble reserved topping evenly over apples and lightly press.
Bake 35–40 minutes until the fruit is bubbling and the top is golden.
Cool in the pan at least 1 hour. Whisk powdered sugar, milk, and a splash of vanilla; drizzle over bars. Chill 30 minutes, then slice.