Place all of the ingredients into a microwave bowl, reserving the vanilla until the end of cooking.
The bowl should be deep enough to allow the mixture to boil, without boiling over.
Cook in the microwave on high for 6½ minutes, stopping to stir halfway through.
The mixture will boil, so handle with care to avoid burning.
After 6½ minutes, stir well coating all of the pecans, then remove from the microwave.
The caramel should be thickened and beginning to form along the sides of the bowl.
If the caramel is still runny, don't panic, it just needs to cook a bit longer.
Microwave in additional 1 minute increments.
Allow to cool on the counter for 15 seconds.
Mix in the vanilla and rum and stir well.
Use a teaspoon, tablespoon or small ice cream scoop to scoop onto buttered wax paper or a silpat.
Immediately sprinkle the tops with sea salt.
[This recipe is based on a 1000 Watt microwave. If your microwave has a lower wattage it may take longer to cook. Likewise, if the microwave has a higher wattage, less cooking time.]
Another technique to test the caramel: Drop a small amount into a glass of ice cold water. If it becomes firm and you can roll it into a ball between 2 fingers, it's ready