Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking dish.

In a large mixing bowl, beat together the butter and granulated sugar until creamy. Add egg and vanilla, blending until incorporated. Mix in flour, baking powder, and salt until soft dough forms. Press into the prepared baking dish.

In another bowl, combine softened butter and powdered sugar, beating until smooth. Add eggs one at a time, mixing well after each. Fold in flour until smooth.

Pour the filling over the pressed dough and drizzle with the salted caramel sauce, swirling gently as desired.

Bake for about 50 minutes, until edges are golden and center is slightly jiggly.

Allow to cool in the pan on a wire rack. Sprinkle with sea salt before slicing.