Line a 9x13'' pan or jelly roll pan with parchment paper. (If you don't have parchment paper you can generously butter the pan.) Either size pan will work--9x13'' will yield thicker caramels.
Add 2 sticks butter, sugar, and karo syrup to a large heavy-bottom saucepan over medium heat. Stir over medium heat until mixture begins to boil, about 5-10 minutes.
Gradually add the evaporated milk, one can at a time, taking about 12-15 minutes PER CAN to slowly add it, while stirring constantly. You want to make sure the mixture maintains a steady heat and constant boil (no drastic changes in temperature) otherwise your caramels can curdle.
Stir the mixture constantly, scraping the sides occasionally until it reaches a firm ball stage (about 240-245 degrees F on a candy thermometer). It takes patience and time, but it's sooo worth it! (Also, I don't really trust or rely on a candy thermometer--I like to test it the old fashioned way. Drop a spoonful of hot caramel sauce into a cup of ice water and mold it with your fingers into a ball. When ready it will feel pretty firm and pliable, but still slightly sticky.)
Once you reach 240-245 degrees F / or the firm ball stage, remove from heat. Stir in vanilla.
Pour caramels into prepared pan. Refrigerate until cooled and hardened. (Best if you refrigerate them overnight, or for several hours. They will be easier to cut and wrap).
The caramel will seem hard in the fridge after they're set, but they should be soft at room temperature. Cut caramel into small pieces and, if desired, wrap like a tootsie roll in wax paper.
Video
Notes
Evaporated milk: Could substitute heavy cream.Troubleshooting:
Candy Thermometer: I don't always trust candy thermometers, and depending on your location (altitude and humidity) temperature will vary. A good way to test them is the ice water method. Drop a spoonful of the hot caramel into a cup of ice water and mold the caramel with your fingers into a ball. The caramel should feel pretty firm but pliable in the ice water.
Caramel is too soft after it has set up: It needed to cook longer. You can pour the whole batch back in to a pot and warm it up again!
Caramel is too hard: it cooked for too long. Use the ice water method to avoid this.
Make Ahead and Storing Instructions: homemade caramels will keep well in the fridge, covered or wrapped, for several weeks. Take them out to come to room temperature for them to be soft and chewy.