In a bowl set over a pan of barely simmering water, melt the dark chocolate and butter, ensuring the bottom of the bowl doesn't come into contact with the water.
Once melted and glossy, pour the chocolate mixture over the caramel.
In another bowl set over barely simmering water, carefully melt the white chocolate. Alternatively, melt the white chocolate in the microwave in 20-second increments. Watch closely, as white chocolate can seize quickly.
Spoon melted white chocolate into a small piping bag and pipe horizontal straight lines about 1/4 inch (6 mm) apart over the dark chocolate. Score the lines using a skewer by dragging it up and down the top of the chocolate, perpendicular to the lines that you piped.
Chill in the fridge until completely set, at least 1 hour or overnight. Remove from the baking pan using parchment paper.
Cut into slices or squares using a sharp, hot knife, wiping between each cut. The espresso millionaire shortbread bars can be stored at room temperature in an airtight container for up to 1 week.