Position a rack in the middle of the oven and preheat to 325°F. Line an 8x8-inch square pan with foil or parchment, leaving an overhang for easy removal; lightly grease the lining.
In a large mixing bowl, beat the room-temperature butter with the granulated sugar until pale and slightly fluffy, about 2–3 minutes using a hand mixer or stand mixer on medium speed. Add the powdered sugar and vanilla and beat just until combined.
Reduce the mixer to low and add the flour in two additions, mixing until a soft, slightly crumbly dough forms. Reserve about half of the dough in a separate bowl for the crumble topping.
Press the larger portion of dough firmly and evenly into the bottom of the prepared pan to form the base (use the back of a spoon or an off-set spatula). Smooth it out so the layer is compact and level.
Bake the crust for 12 minutes, just until the edges begin to set and the surface looks drier but not browned. Remove from the oven and let the par-baked crust cool on a rack for 5 minutes.
While the crust cools, fold the chocolate chips into the reserved dough. Chill that dough bowl in the refrigerator for about 20–30 minutes — this firms the crumble so it holds some texture when baked.
Warm the caramel sauce briefly (10–20 seconds in the microwave, stirring once) until pourable but not hot. Pour it onto the warm crust and spread to an even layer with an offset spatula, leaving a small margin at the edges.
Crumble the chilled chocolate-chip dough over the caramel in coarse pieces so some caramel peeks through. Sprinkle the flaky sea salt evenly over the top.
Return the pan to the oven and bake 20–24 minutes, until the topping is golden and set at the edges (the center may still look slightly soft). Remove from the oven and cool completely on a wire rack.
Once cooled to room temperature, refrigerate the pan for at least 30–60 minutes to firm the caramel for cleaner slices. Use the foil overhang to lift the slab from the pan and cut into 16 bars with a sharp knife.