1. Blend coconut milk, avocado, lime, and sugar to a smooth puree in a bar blender. Add the puree to a stand mixer with the paddle attachment.
2. Slowly churn with the paddle attachment and very slowly pour in liquid nitrogen.
3. If the mixture starts to stick to the sides, use a blowtorch on the bowl to release the ice cream.
4. Once completely frozen, transfer to a container and place in the freezer.
5. Remove from the freezer 20-25 minutes before serving, to soften.
1. Heat the sugar and rum in a pan over medium heat until sugar has dissolved, then add the pineapple and cook for 5 minutes.
2. Toss and cook for 5 more minutes at a gentle simmer, until tacky but not sticking. Remove the pineapple from the syrup.
3. Remove the pan from the heat and swirl in the butter to make a glaze, then return the pineapple to the sauce and turn to coat.
4. Serve the glazed pineapple warm or at room temperature (not cold or butter will solidify) over the ice cream.
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