Melt butter and stir in sugars, cream, and corn syrup, stirring occasionally until sugars have dissolved.
Clip a candy thermometer to the side of the pan. Reduce heat and stir occasionally until thermometer registers 248 degrees.
Remove mixture from heat, mix in vanilla extract, and quickly pour caramel mixture into a 9x9-inch baking pan lined with parchment paper. Allow caramel to stand for 2 hours, or until firm.
Lift caramels out of pan and use a buttered knife or a knife coated with nonstick cooking spray to cut cooled caramels.
Wrap each caramel in waxed paper or plastic wrap. Store at room temperature for up to 2 weeks.