Prep the oven: Preheat to 350°F (175°C). Line an 8x8-inch pan with parchment paper, leaving a little overhang for easy removal.
Make the crust & crumb: In a large bowl, whisk together the flour, baking powder, salt, and both sugars. Cut in the cold butter using a pastry cutter or your fingertips until the mixture resembles coarse crumbs. Stir in the egg and vanilla until combined and clumpy (Whisk the egg and vanilla together before adding).
Form the base: Press about two-thirds of the crumb mixture into the bottom of your prepared pan to form an even crust. Set the remaining third aside for the topping.
Cook the apple filling: In a medium saucepan over medium heat, combine chopped apples, sugar, lemon juice, cinnamon, salt, and vanilla. Cook for 4–5 minutes, stirring often, until the apples start to soften and release juices.
Make the slurry: In a small bowl, whisk the cornstarch with 2 tablespoons of water until smooth. Stir the slurry into the apple mixture and cook for another 1–2 minutes, until thickened. Remove from heat and let cool for 5 minutes.
Assemble: Spread the apple filling evenly over the crust. Crumble the reserved dough mixture over the top.
Bake: Bake for 40–45 minutes, until the top is lightly golden and the filling is bubbling around the edges.
Cool: Let the bars cool completely in the pan. For clean slices, chill in the fridge for 1–2 hours before cutting.
Serve: Slice into squares and enjoy as is—or warm slightly and top with a scoop of vanilla ice cream for extra coziness.