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Pour the tuna into a fine wire mesh sieve and allow to thoroughly drain.
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Once the tuna has fully drained, add it to a large bowl.
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Pour the cognac over the tuna and using a fork, mix it in, breaking up the really large chunks.
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Cover and chill for 30 minutes.
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Melt butter in a pan over medium heat and sauté the diced shallots until soft, about 5 minutes.
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Add the shallots and remaining melted butter to the tuna along with the liquid bacon renderings, parsley, salt and pepper. Mix well, taking care to blend all the ingredients together. Cover and chill for at least one hour.
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Remove the endive leaves from the stalk, clean, and trim.
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Spoon the tuna rillettes into the individual leaves.
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Garnish with the optional ingredients, if desired.