First, brown the butter. In a small saucepan over medium-low heat, melt all of the butter and stir constantly until melted and simmering. Continue to simmer, on medium heat, for at least a few minutes, until the popping and hissing sounds have completely subsided (this is the water in the butter burning off – you’ll know once it’s silent). Continue to cook, stirring constantly, until the butter reaches a deep amber color and smells nutty or caramelly. Once it reaches that color, immediately take off the burner and let sit until cool (or pop in the fridge to cool faster).
Meanwhile, lightly grease a 9x13 inch pan, line with parchment paper, and grease again. Preheat oven to 350° Fahrenheit. Once the butter is cool and room temperature (solidified), make the shortbread. In a large bowl, using an electric mixer, beat together the browned butter and sugar until creamy and fluffy. Add in the vanilla and beat until combined. In a smaller bowl, whisk together the flour, starch, and salt, then dump ingredients into the butter/sugar bowl and stir together with a spatula until the dough comes together. It will be fairly crumbly and should not be sticky or wet. Press the dough into the prepared pan until you have an even layer of shortbread across the bottom. Bake for 30 minutes until edges are just golden brown. Remove from oven and let cool completely.
Make the caramel layer. Hook your candy thermometer onto the edge of a large saucepan so that the bottom tip of the thermometer nearly touches the bottom of the pan. Pour the two cans of condensed milk in, along with the butter, corn syrup, salt, and sugar. Heat on medium-low, stirring constantly, until everything is melted and combined. Continue to stir for 10-20 minutes to let the caramel thicken, darken, and soak up the butter (it will look buttery and curdled for a while, keep stirring and cooking!). Cook until the thermometer reaches between 220-225° Fahrenheit then remove from heat immediately, add in the vanilla, and stir until it stops bubbling, then quickly pour caramel over the cooled shortbread, spreading it evenly over the shortbread to the corners.
Then melt your chocolate. Chop chocolate into small pieces and melt in a microwave or over a double boiler in short spurts until fully melted. Pour chocolate over caramel layer and again spread evenly to the corners. Then let cool! You can pop this in the fridge to harden the chocolate layer, for about 30 minutes. Then lift the entire thing out with the parchment paper and slice into desired size bars for your guests!