Step 1

Preheat the oven to 350°F and set an oven rack in the middle position. Line a 9-inch square pan with aluminum foil, pushing the foil neatly into the corners and up the sides of the pan, using two pieces if necessary to ensure that the foil overlaps all edges (the overhang will help removal from the pan). Spray the foil with nonstick cooking spray or grease with butter.

Step 2

In the bowl of a food processor fitted with a metal blade, combine the flour, brown sugar, cornstarch, and salt; process until well combined and no lumps of sugar remain. Add the butter and egg yolk; process for 10 to 15 seconds, until a coarse meal forms. Add the ice water and blend until you have a moist, crumbly dough, about 10 seconds more. Dump the dough into the prepared pan and press with your fingers into an even layer (dust your fingers with flour if the dough is too sticky). Prick the dough all over with a fork and bake until golden, about 20 minutes. Set aside to cool.

Step 3

In a medium, heavy-bottomed saucepan over medium heat, melt the butter. Add the sweetened condensed milk, heavy cream, corn syrup, vanilla, brown sugar, and salt, whisking until evenly combined. Bring to a simmer and continue cooking, stirring frequently, until the mixture registers between 236°F and 239°F on an instant-read digital thermometer, 10 to 20 minutes. (Note: It's important to use an instant-read thermometer, rather than a clip-on candy thermometer, as temperatures can vary in different spots of the caramel. An instant-read thermometer allows you to test the temperature in multiple areas for accuracy; aim for an average if the readings differ.) Once the caramel reaches the desired temperature, carefully pour it over the crust—remember, it’s extremely hot. Tilt the pan to spread the caramel evenly. Let sit for 30 to 35 minutes, until the caramel layer is set but still slightly warm. (See note below on cleaning the pot.)

Step 4

Place the semi-sweet and milk chocolate in a small microwave-safe bowl. Microwave in 20-second bursts, stirring in between, until the chocolate is about 75% melted. Continue melting in 5 to 10 second-bursts, stirring in between until the chocolate is melted and smooth. Do not overheat or the mixture will break.

Step 5

Using an offset spatula, spread the chocolate evenly over the caramel layer. Refrigerate until the bars are cold and the chocolate is set, 1½ to 2 hours. Let the bars sit out for 10 to 15 minutes to soften the chocolate slightly. Lift the bars out of the pan using the foil overhang and transfer to a cutting board. Using a sharp knife, cut into small squares (if the chocolate seems brittle, let the bars sit at room temperature a bit longer before cutting). Sprinkle the bars with flaky sea salt. Store in the refrigerator; serve cold or slightly chilled.