Line an 8 x 8-inch pan with non-stick foil and set aside.
In a large, heavy saucepan, combine the sugar, brown sugar, corn syrup, half and half, whipping cream, and butter. Stir well to combine all the ingredients.
Place the saucepan over medium-low heat and cook, stirring constantly, until the mixture reaches 250ºF on a candy thermometer.
Once it reaches 250ºF, remove the pan from heat and add the vanilla.
Pour the hot caramel into the prepared pan and let cool completely at room temperature.
Cut the cooled caramels into small squares and wrap in waxed paper.