Prepare the Pan
Line your 8x8 or 9x13-inch baking dish with parchment paper, allowing some overhang on two sides. Lightly grease the parchment paper with butter or cooking spray.
Combine and Begin Cooking
In the heavy-bottomed saucepan, combine the butter, brown sugar, granulated sugar, light corn syrup, and sweetened condensed milk. Place the saucepan over medium heat.
Stir and Dissolve
Stir constantly until the butter is melted and the sugars are completely dissolved into the mixture. Once the mixture comes to a full boil, continue to stir to prevent the bottom from scorching.
Monitor Temperature
Attach the candy thermometer, ensuring the tip is submerged but not touching the bottom of the pan. Continue cooking and stirring until the mixture reaches 248°F (Firm Ball Stage). This may take 25–30 minutes; do not increase the heat.
Finish and Pour
Immediately remove the pan from the heat once it hits 248°F. Stir in the vanilla extract (it will bubble vigorously). Pour the caramel into the prepared pan. Do not scrape the sides or bottom of the pan.
Cool and Cut
If using, sprinkle the flaky sea salt over the top while the caramel is still warm. Allow the caramel to cool and set completely at room temperature for at least 4 hours, or until very firm. Lift the slab out using the parchment overhang. Cut into small squares using a sharp, buttered knife.
Wrap and Store
Wrap each caramel individually in small squares of wax paper or parchment paper. Store in an airtight container at room temperature for several weeks.