Preheat the oven to 350°F (175°C). Line an 8x8-inch pan with parchment paper, leaving overhang for easy lifting.
Lightly grease the sides.
Make the crust/crumble: In a large bowl, whisk flour, oats, brown sugar, baking powder, salt, and cinnamon. Stir in melted butter and vanilla until the mixture looks sandy and clumps when pressed.
Press 2/3 of the mixture firmly into the pan to form an even base. Use the bottom of a measuring cup to pack it down well.
Reserve the remaining 1/3 for the crumble.
Make the apple filling: In a medium bowl, combine apples, granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, cornstarch, and a pinch of salt. Toss until the apples are evenly coated.
Layer the apples evenly over the crust, spreading them to the edges. Sprinkle the reserved crumble over the apples, squeezing small handfuls to form chunky pieces.
Bake for 35–42 minutes, until the top is golden and the apples are bubbling at the edges.
If the top browns too quickly, tent loosely with foil.
Cool the pan on a rack for at least 1 hour to set. For the cleanest slices, refrigerate 30–60 minutes before cutting into bars.
Finish as you like: Dust with powdered sugar, drizzle with caramel, or serve warm with ice cream.