Preheat the oven to 325°F (165°C). Line a 9x13-inch metal baking pan with parchment paper, leaving overhang on two long sides to create a sling. Lightly grease the parchment and any exposed sides of the pan with butter or non-stick spray.

In a large mixing bowl, beat the softened butter for the shortbread base until smooth and creamy. Add the granulated sugar and powdered sugar and beat on medium speed until light and fluffy, about 2–3 minutes. Mix in the vanilla extract and fine sea salt.

Turn the mixer to low and gradually add the all-purpose flour, mixing just until a soft dough forms. The dough will look a bit crumbly but should hold together when pressed between your fingers. If it seems very dry, you can add 1–2 teaspoons of milk, a little at a time, until it comes together.

Transfer the shortbread dough into the prepared pan. Use your hands or the bottom of a measuring cup to press it into an even, compact layer, paying attention to the corners so the base is as level as possible.

Bake the shortbread for 20–25 minutes, or until the edges are just turning light golden and the top looks set. The shortbread should be pale and just cooked through, not deeply browned. Remove the pan from the oven and let it cool slightly while you prepare the caramel layer.

In a medium heavy-bottomed saucepan, combine the sweetened condensed milk, butter pieces for the caramel, packed light brown sugar, light corn syrup or golden syrup, and fine sea salt. Set the pan over low to medium-low heat and stir frequently until the butter is melted and the mixture is smooth.

Increase the heat slightly to medium and cook the caramel mixture, stirring almost constantly, for about 10–15 minutes. The caramel will thicken and deepen from pale to a rich golden color. It is ready when it pulls away from the sides of the pan as you stir, leaves a clear trail when you drag a spatula across the bottom, and a small spoonful dropped on a plate holds its shape after a minute or two. If using a thermometer, aim for about 225–235°F (soft ball stage).

Remove the saucepan from the heat and stir in the vanilla extract for the caramel. Carefully pour the hot, thick caramel over the baked shortbread base. Use a spatula to spread it into an even layer, making sure it reaches all the corners.

Let the pan cool at room temperature for 20–30 minutes, then transfer it to the refrigerator for 1–1 1/2 hours, or until the caramel is firm but still slightly soft when gently pressed with a fingertip. Do not rush this step; the layers will slice more cleanly if the caramel is well set.

Place the chopped semi-sweet or dark chocolate in a heatproof bowl. Melt it in the microwave in 20–30 second bursts, stirring between each, or over a double boiler set over gently simmering water. When the chocolate is almost completely melted, remove from the heat and stir until smooth, then mix in the neutral oil until glossy.

Remove the pan from the refrigerator and make sure the caramel layer is firm. Pour the melted chocolate mixture over the caramel, tilting the pan and using an offset spatula to spread it into an even layer. If using flaky sea salt, sprinkle it over the chocolate while it is still wet.

Let the bars sit at room temperature for 20–30 minutes, then refrigerate for another 30–45 minutes, until the chocolate is mostly set but not rock-hard. This semi-set stage helps the chocolate cut cleanly without cracking.

Use the parchment sling to lift the entire slab of millionaire’s shortbread out of the pan and onto a cutting board. Run a sharp knife under hot water, wipe it dry, then cut into 24 large bars or up to 36 smaller squares or rectangles. Wipe and rewarm the knife between cuts for the cleanest layers.

Serve the millionaire’s shortbread at cool room temperature so the shortbread is tender, the caramel is thick but silky, and the chocolate has a pleasant snap.