Add pomegranate juice to a saucepan and place it over medium heat on the stove. Pour in honey and lime juice and stir to combine. Let the mixture simmer for approximately 25-30 minutes, or until it reduces to ½ cup of thick, syrupy liquid.
Remove from heat and let it cool completely before transferring it to a glass jar for storage.
Now make the Agrodolce
Pour the vinegars and honey in a medium saucepan and set it on the stove. Turn the heat up to medium-low and stir frequently to dissolve honey. Let the liquid simmer for 10 minutes before adding pomegranate molasses. Stir until the mixture is smooth.
Let it simmer for an additional 5 minutes or until you are left with a little over a cup of thick, syrupy liquid.
Store in a Mason type glass jar in the refrigerator.
This delectable sauce can be served warm or chilled over a wide range of dishes, including grilled meats, salads and even desserts.
Of course, it can also be enjoyed by the spoonful straight from the jar (just don't tell anybody I said that...)