Peel and core the pineapples, then finely chop the flesh.
Place the pineapple, brown sugar and sea salt in a large, wide, heavy-based saucepan or preserving pot.
Cook uncovered over medium-high heat for approximately 25–35 minutes, stirring regularly. The pineapple will initially release its juices. Continue cooking until much of the liquid evaporates and the fruit becomes golden and caramelised.
If your saucepan is not wide enough for the pineapple to caramelise properly, cook it in batches before returning everything to the pot.
Reserve approximately 4 tablespoons of the caster sugar and mix it thoroughly with the powdered pectin.
Add the remaining caster sugar and fresh lime juice to the caramelised pineapple. Stir over medium heat until the sugar dissolves.
Mash gently or blend briefly with a stick blender until the jam reaches your preferred consistency.
Bring to a steady boil and cook for approximately 15–25 minutes, stirring frequently to prevent the bottom from catching.
Gradually sprinkle in the pectin mixture while stirring continuously.
Return to a full boil and cook for approximately 2–3 minutes, or as directed on the pectin packet.
Test a spoonful on a chilled plate. After cooling for a minute, it should wrinkle slightly when pushed with your finger.
Remove from the heat and stir in the lime zest and vanilla bean paste.
Divide between approximately 12 clean, sterilised small jars and seal.
Refrigerate once cooled or follow an appropriate tested water-bath preserving process if preparing jars for pantry storage.