In a large pot add sweetened condensed milk, dark brown sugar, salted butter, and corn syrup. Cook over medium to medium-high heat. Stir constantly to avoid bottom from burning.
Mixture will begin to bubble and increase in volume. Avoid scraping sides of pan as this can make the caramel crystallize during the cooling phase (and go "grainy" or "sugary.") Using a calibrated candy thermometer, cook mixture to 234-238 degrees F or soft ball stage (depending on how soft you want your caramels to be).
You can test how soft or firm it is by dipping a spoonful into a cup of ice water to cool quickly.
Remove from heat and add vanilla.
Pour into a butter greased 9x13 inch pan. Pour quickly and DO NOT scrape sides of pan (this can cause the caramel to crystallize and go grainy also.
Once cooled, wrap individual pieces in waxed paper or use in other recipes that call for caramel. Store in an airtight container or bag. Will keep for several weeks if kept in a cool, dry place.