Insert a licorice stick, cinnamon stick, or bamboo skewer into the stem end of each apple and pear. Spread the granola on a baking sheet; reserve. Have ready 1 or more cooling racks or a large sheet of parchment paper for cooling the caramel fruits.
In a saucepan over low heat, combine the sugar, corn syrup, vanilla extract, and water. Cook, stirring, until the sugar melts. Add the butter and cream, raise the heat to medium-high, and bring to a boil. Cook, stirring occasionally, until the caramel registers 240 degrees F on a candy thermometer, about 10 minutes. Remove from the heat and let cool for 2 minutes.
One at a time, dip the apples and pears in the caramel, twirling and swirling them to coat completely. Dip the tops in the granola to coat them, then transfer to the cooling rack or the parchment paper to cool. As the apples and pears cool, the caramel will set. Store the caramel apples and pears, wrapped in cellophane if desired, in a cool, dry place until ready to serve or up to 2 days.