Heat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving overhang on the two long sides for easy lifting.
Make the crust: whisk the flour, granulated sugar, and salt in a large bowl. Cut in the cold butter with a pastry cutter (or pulse in a food processor) until the mixture looks like coarse crumbs. Press the crumbs firmly and evenly into the bottom of the prepared pan, using the bottom of a measuring cup to pack them flat.
Bake the crust for 15 minutes, until the edges are just starting to turn golden. Set aside while you make the filling — leave the oven on.
Make the filling: toss the sliced apples with the granulated sugar, brown sugar, flour, cinnamon, nutmeg, lemon juice, and vanilla in a large bowl until the apples are evenly coated.
Make the crumble: stir the flour, oats, brown sugar, cinnamon, and salt together in a medium bowl. Work in the cold butter with your fingertips or a pastry cutter until the mixture forms pea-sized clumps that hold together when squeezed.
Spread the apple filling evenly over the warm crust, then sprinkle the crumble over the top, covering the apples completely.
Bake for 40 to 45 minutes, until the topping is deep golden and the apple filling is bubbling at the edges.
Cool completely in the pan on a wire rack, at least 2 hours, before slicing — the bars need this time to set or they will fall apart.
Lift the bars out of the pan using the parchment overhang. Slice into 24 squares with a long, sharp knife, and drizzle with salted caramel sauce before serving, if you like.