Preheat your oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out after baking.
In a large bowl, beat the softened butter and sugars together until light and fluffy, about 2-3 minutes. Add the vanilla extract and salt, then gradually mix in the flour until just combined.
Press the dough evenly into the prepared pan. Use the bottom of a measuring cup to smooth the surface. Bake for 15-18 minutes until lightly golden around the edges.
While the crust is baking, toss the sliced apples with lemon juice in a large bowl. In a separate small bowl, whisk together the sugar, flour, cinnamon, nutmeg, and salt. Sprinkle this mixture over the apples and toss until evenly coated.
In a medium bowl, combine the brown sugar, flour, oats, cinnamon, and salt for the streusel topping. Add the cold cubed butter and use a pastry cutter or your fingers to work the mixture until it resembles coarse crumbs with pea-sized butter pieces.
Arrange the apple filling in an even layer over the par-baked crust. Sprinkle the streusel topping evenly over the apples.
Bake for 40-45 minutes, or until the filling is bubbling and the streusel is golden brown. If the topping starts browning too quickly, loosely cover the pan with aluminum foil for the remaining bake time.
While the bars are baking, make the salted caramel sauce. In a medium saucepan, heat the sugar over medium heat, stirring constantly with a heat-resistant spatula. The sugar will form clumps before melting into an amber-colored liquid.
Once completely melted, immediately add the butter (be careful, it will bubble vigorously!). Whisk until the butter is fully incorporated, then remove from heat and slowly pour in the heavy cream while whisking constantly. Stir in the vanilla and salt. Allow the caramel to cool slightly before using.
Allow the bars to cool completely in the pan on a wire rack, about 2 hours.
Once cooled, drizzle with the salted caramel sauce and sprinkle with additional flaky sea salt if desired. Use the parchment overhang to lift the bars out of the pan and cut into 16-20 squares.