If using an ice cream maker with a frozen insert, freeze the insert for at least 24 hours. For the alternate pan method, place an 8-by-8-inch freezer-safe pan in the freezer about 1 hour before blending.

Pour the filtered water into a stainless one-quarter-cup measure or small bowl. Sprinkle the gelatin evenly over it and let it stand until the granules are swollen and translucent with no dry powder.

Transfer the gelatin bloom to a small stainless saucepan. Warm over the lowest heat, stirring gently, just until clear and fully fluid. Remove before simmering and let cool briefly while keeping it pourable.

Put the watermelon, homemade coconut milk, and homemade vanilla in the true-size Ninja BN801 pitcher. Blend on low just until the watermelon disappears and the mixture is evenly coral-pink with tiny natural fruit flecks.

With the blender running on low, pour in the cooled dissolved gelatin in a thin stream. Blend only a few seconds after the last of it goes in, until no clear ribbons, white coconut streaks, or gelatin threads remain.

Start the assembled machine and pour in the blended base. Churn until the mixture is thick enough to mound against the paddle and a spoonful holds a soft rounded ridge. Serve soft or transfer to a covered freezer-safe container for a firmer scoop.

Pour the blended base into the prechilled 8-by-8-inch pan. Freeze and stir thoroughly every 20 minutes, scraping the frozen edges into the softer center, until the sherbet reaches the firmness you prefer.