Prepare the Pan: Line a 9x13-inch baking dish with parchment paper, leaving an overhang on each side for easy removal. Lightly grease the parchment paper to prevent sticking.
Cook the Sugar Mixture: In a large, heavy-bottomed saucepan, melt butter over medium heat. Add granulated sugar, brown sugar, corn syrup, sweetened condensed milk, and heavy cream. Stir constantly until sugars dissolve and the mixture starts to boil.
Boil to Firm-Ball Stage: Attach a candy thermometer to the saucepan and continue cooking, stirring occasionally, until the mixture reaches 248°F (120°C), which is the firm-ball stage.
Add Almonds and Vanilla: Remove from heat and stir in chopped almonds, vanilla extract, and salt until well combined.
Pour and Cool: Pour the hot caramel into the prepared baking dish, spreading it evenly. Let it sit for a few minutes.
Top with Sea Salt: Sprinkle the top of the caramel with flaky sea salt.
Set and Cut: Allow the caramels to cool completely at room temperature, then refrigerate until firm. Use the parchment paper overhang to lift the caramel slab out of the pan, then cut into small squares.