Prepare the cookie. Preheat the oven to th. 7 (210°C).
Separate the egg yolks from the whites. Whisk the yolks with 100 g of sugar until the mixture whitens. Add the flour and then the beaten egg whites with a pinch of salt.
Pour the mixture onto a sheet of buttered parchment paper placed on a baking sheet. Smooth the top with a spatula. Bake for 7 to 8 minutes. When the biscuit is cooked, turn it over on a damp cloth. Remove the parchment paper. Roll the biscuit widthwise. Leave to cool.
Prepare the mousse:peel the pineapple, then mix its pulp to obtain 300 g of puree. Whisk the egg yolks and 75 g of sugar until the mixture whitens and doubles in volume. Soften the gelatin sheets in cold water. Dissolve the cornstarch in 2 tablespoons of water, add it to the egg-sugar mixture as well as the pineapple purée. Cook this preparation over low heat, stirring until the preparation coats the spoon. Remove from the heat, add the drained gelatine sheets, mix. Put in the fridge and let set. Whip the whipped cream with 25 g of sugar. Incorporate it into the mousse.
Make a syrup with 10 g of sugar, 10 cl of water and the rum. Unroll the biscuit and soak it with syrup. Spread the pineapple mousse. Roll the biscuit into a log and keep it cold.
Peel the pineapple. Cut it into slices. Brown them in a pan with 150 g of sugar. Cut them into 6. Take out the rolled log. Heat the honey. Spread it over the entire surface of the log. Sprinkle with grated coconut, pomegranate seeds and pineapple wedges.
Serve the log very cold.