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Split the egg yolks and whites and add 4 egg yolks to a medium-sized bowl. Keep 2 egg whites aside to use later on. Drain the pineapple and pour 100 ml of the syrup/juice into a medium-sized pan.
Add the milk and heat on low heat. Meanwhile chop half of the pineapple into small pieces and keep the other half aside for serving. Beat the egg yolks with a whisk for a few minutes until they're a bit fluffy and pale.
Pour a bit of the warm milk mixture into the yolks and keep on whisking to prevent it from creating lumps. Gradually pour in the rest of the milk and as soon as the mixture is smooth you can transfer it all back to the pan.
Heat the mixture on low heat to cook the egg yolks. Keep stirring, it's best to use a silicone spatula to do this to prevent the mixture from burning.
You'll notice the mixture will starting to become thicker.
Soak 4 gelatin leaves in cold water, squeeze most of the water out of the gelatin and dissolve them into the milk and egg yolk mixture. Stir in a tablespoon of rum and let it cool off a bit.
Beat the heavy cream until it has about the thickness of yogurt and add it to the milk mixture. Also add the chopped pineapple. Beat the egg whites until they form stiff peaks and then gradually add 40 gram sugar.
Carefully add the egg whites to the mixture, make sure it won't loose too much of its fluffiness. Divide the bavarois over small bowls and refrigerate overnight.
You can serve a bavarois in its bowl, but you can also unmold it onto a plate. The easiest way to unmold them is dipping the plastic bowls into hot water. Serve with the rest of the pineapple chunks, enjoy!