Prepare the pan. Line an 8x8 cake pan with two pieces of parchment paper, leaving a 1-2 inch overhang. Set aside.
Combine the ingredients. To a heavy bottomed pot, add the cream, butter, sugar, corn syrup, and ½ teaspoon of salt. Stir to moisten all the sugar, then place the pan over medium heat, stirring regularly until the butter is melted.
Bring to a boil. Once the butter has melted, increase the heat to medium-high. When it comes to a boil, reduce the heat to medium to maintain a low boil. Clip the candy thermometer to the side of the pan, making sure the tip does not touch the bottom.
Cook to firm ball stage. Continue to cook the mixture, stirring regularly, until the temperature reaches 245°F on the thermometer, or the firm ball stage, 30-40 minutes. The mixture will darken slightly to a deep honey color.
Add vanilla and pour. Off the heat, add the vanilla extract and stir to incorporate. The mixture will bubble. Pour the hot caramel into the prepared pan.
Salt and cool. Cool for 10-15 minutes, then sprinkle with ¼ to ½ teaspoon of flaked salt. Continue to cool at room temperature for 2-3 hours.
Cut the caramels. Lift the cooled caramel out of the pan using the parchment overhang and place on a cutting board. Using a sharp knife, cut into 8 one-inch-wide strips, then cut the strips into 1-inch segments for 64 caramels.