Collect 4 cups of watermelon juice by placing a large colander in a large bowl.

Cut the watermelon in half and scoop out melon chunks into the colander.

Slash through the chunks or press gently to extract juice into the bowl.

Take the chunks from the colander and pulse in a food processor until nearly pureed in batches.

Pour the puree through a sieve and add to the watermelon juice in the bowl.

Measure out 4 cups of watermelon juice and reserve the remainder.

Add simple syrup and lemon/lime juice to the measured juice.

In a small bowl, whisk the egg white with about a half cup of the juice mixture until frothy.

Add the frothy egg white mixture back to the juice mixture.

Set aside 3/4 cup of the mixture and store in the refrigerator.

Pour the remaining mixture into a large flat pan (e.g., 9x13 pyrex baking pan) and place in the freezer until frozen solid.

Once frozen, let it sit for 5-10 minutes at room temperature, then start gouging with a spoon.

Put chunks in a food processor or blender.

Take out the reserved 3/4 cup from the fridge and pour a small quantity over the chunks.

Pulse a few times. If the mix is too solid, let it sit a little longer and loosen with a spoon. Add more liquid mix as needed.

Process until the mix starts whirling and becomes smooth.

Immediately pour the pureed mixture into a container with a lid and allow to firm up in the freezer for about an hour or so.