1. Butter a parchment paper lined 8 ½ x 12-inch baking pan and set aside.
2. Place butter into bowl with the mixer blade. Mix at speed 3, temperature 270°F for 2 minutes and 30 seconds or until butter is melted. Add brown sugar and salt. Mix at speed 3 and 270°F for 2 minutes and 30 seconds; scrape sides.
3. Add corn syrup and mix at speed 3, temperature 270°F for 13 minutes or until mixture boils. Add sweetened condensed milk. Make sure stopper is set on closed for steam. Mix at speed 3, temperature 270°F for 1 hour or until temperature of caramel mixture reaches 243°F to 244°F (using a digital candy thermometer if possible). Start checking temperature with 5 minutes left of cooking time. Once proper temperature is reached, add vanilla; mix well.
4. Carefully pour extremely hot caramel into prepared pan and cool completely. Once cooled, carefully remove caramel slab from pan onto a cutting board and remove parchment paper. Using a sharp knife or pizza cutter, cut caramels into 1-inch pieces and wrap with candy wrappers, waxed paper, or plastic wrap.