Heat a saucepan that will hold the shells in a single layer over medium-high heat, add 1 tbsp of oil and the knob of butter. When hot add the shells and using the end of a rolling pin bash the claws and heads so that all the juice comes out, fry for 10-15 minutes, stirring, as it catches and caramelises. When well-coloured remove to a bowl.
Deglaze the pan with the rum, scraping to release the bits at the bottom of the pan, then add to the bowl with the shells.
Return the pot to the stove over medium heat, add the remaining tbsp of oil and when hot, add the onion, carrot, garlic and coriander stems. Fry until golden, about 10 minutes. Then add the tomato puree and cook until amalgamated with the oil, about 2 minutes.
Add the shells back to the pot and then add the water, salt and avocado leaf, plus a cracked piquín or two. Bring to a boil then reduce to a mere simmer for an hour or so. Strain the broth and discard the shells and vegetables.
Serve hot in small shot glasses with a cracked Chile Piquín on top and a wedge of lime.