Preheat your oven to 350°F (175°C) and line a 9×13-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
In a large bowl, cream together the softened butter and both sugars until light and fluffy, about 3 minutes. Add the vanilla extract and mix well.
Gradually add the flour and salt, mixing until just combined – overmixing will make your shortbread tough rather than tender.
Press the dough evenly into the prepared pan. For a perfectly even base, use the bottom of a measuring cup to smooth the surface. Bake for 15 minutes until the edges are just beginning to turn golden. Remove from the oven but keep the oven on.
While the crust bakes, peel, core, and thinly slice the apples (aim for slices about 1/4-inch thick). In a large bowl, toss the apple slices with lemon juice to prevent browning.
Add both sugars, flour, and spices to the apples, tossing until the apples are evenly coated.
In a medium bowl, combine the oats, brown sugar, cinnamon, and flour for the crumb topping. Using your fingers or a pastry cutter, work the cold butter into the mixture until it resembles coarse crumbs with some pea-sized butter pieces remaining.
Layer the spiced apple slices evenly over the par-baked crust, then sprinkle the crumb topping evenly over the apples.
Return the pan to the oven and bake for 40-45 minutes, until the topping is golden brown and the filling is bubbly around the edges.
While the bars are baking, make the caramel sauce. In a medium saucepan over medium heat, melt the sugar, stirring constantly with a high-heat resistant spatula. The sugar will form clumps before melting into an amber-colored liquid.
Once the sugar is completely melted, immediately add the room temperature butter (be careful, it will bubble vigorously). Whisk until the butter is fully incorporated, about 2 minutes.
Very slowly drizzle in the heavy cream while whisking constantly. Allow the mixture to boil for 1 minute, then remove from heat and stir in the vanilla and sea salt. Let the caramel cool for about 15 minutes before using.
Allow the bars to cool completely in the pan on a wire rack, about 2 hours.
Once cooled, use the parchment overhang to lift the entire dessert out of the pan. Drizzle generously with the salted caramel sauce and sprinkle with additional flaky sea salt if desired.
For clean, precise cuts, refrigerate for 30 minutes after adding the caramel, then use a sharp knife dipped in hot water and wiped clean between cuts.