Place a popsicle stick into the top center of each pear. Set them aside. Lay out a sheet of wax paper on a flat surface. In a small pot bring the butter, brown sugar, dark corn syrup, and sweetened condensed milk to a boil over medium heat, stirring every few minutes. Continue cooking until the temperature of the mixture reaches 250 degrees Fahrenheit with a candy thermometer, stirring every minute or two. Remove the pan from the heat and stir in the vanilla extract and salt.

To dip the pears in the caramel, you can either hold the pear slightly sideways and turn it over the caramel until it is covered, or fill a large mason jar or glass about 2/3 full with the caramel sauce and dip the pear in it vertically, leaving about 2 inches of headspace on the pear. Hold the pear over the caramel sauce for 20-30 seconds, allowing the excess caramel to drip off. Then place the pear on the sheet of wax paper and allow it to cool to room temperature. Before serving, grab the un-carameled top of the pear and pull out the popsicle stick, then replace it with the decorative branch (optional).