In a medium saucepan, bring the pomegranate juice to a boil, then reduce to a simmer. Let it simmer for about one hour, occasionally scraping down the sides of the pot.
While the pomegranate juice is reducing, prepare the rest of your ingredients. Grease an 8×8-inch pan or loaf pan, and line it with two strips of parchment paper, ensuring the bottom and sides are covered. Cut 32 pieces of wax paper into roughly 4-inch squares for wrapping the caramels later.
Cook the pomegranate juice down until it turns into a slightly thick, syrup-like consistency and yields about ½ cup. To check the consistency, swipe your finger across a rubber spatula—if it feels thick and syrupy, it’s ready.
Once the pomegranate juice has reduced, add the butter, granulated sugar, brown sugar, and heavy cream to the saucepan. Stir to combine.
Turn the heat to medium and allow the mixture to come to 255-260°F (123-127°C), stirring occasionally. Use a candy thermometer to monitor the temperature.
Once the caramel reaches the desired temperature, remove it from the heat and stir in the vanilla and sea salt. If using red food coloring, add a small amount at a time and stir until the desired color is reached.
Pour the caramel into the prepared pan and place it in the fridge, uncovered, for about two hours until set.
Once the caramel has solidified, lightly coat the blade of a sharp chef’s knife with neutral oil and cut the caramel into your desired sizes. Add a bit of oil to the knife between each cut to prevent sticking.
Separate the caramels immediately to prevent them from sticking together, and wrap each piece individually in wax paper.