Attach a candy thermometer to a large pot. Place butter, sugars, corn syrup, and heavy cream in pot and turn heat to medium. Stir ingredients and bring mixture to a simmer. Raise temperature to medium / medium high (slightly higher) and bring to 240 degrees. It may take 20-30 minutes to bring to temperature. Watch carefully and do not walk away from stove, this can burn easily.
Once mixture is 240 degrees, remove from heat and add vanilla, stir and let cool for a minute. Pour hot mixture into greased glass pan to set. Let set for a few hours. Caramel will continue to set the longer it sits, I like letting it sit for 8 hrs or overnight.
For a softer caramel add 1/2 cup more heavy cream and bring to 135 degrees. For a harder caramel, bring to 145 degrees or higher.