Preheat oven to 350°F. Line a 9×13-inch pan with parchment, leaving overhang.
Whisk flour, oats, brown sugar, half the granulated sugar, baking powder, salt, and 1½ tsp cinnamon in a bowl.
Pour in melted butter and vanilla. Stir until the mixture forms moist, sandy clumps.
Press about two-thirds of the mixture firmly into the prepared pan to form the crust. Reserve the rest for topping.
Toss diced apples with lemon juice, remaining granulated sugar, remaining ½ tsp cinnamon, nutmeg, and cornstarch.
Spread the apple mixture evenly over the crust.
Fold chopped walnuts into the reserved crumb and sprinkle evenly over the apples.
Bake 38–45 minutes, until the topping is deep golden and the filling is bubbling at the edges.
Cool completely in the pan. Chill 1 hour for cleaner slices, then lift out and cut into bars.