Add the cubed, deseeded watermelon to a blender and process for approximately 30 seconds until you have a completely smooth juice. If you want an even smoother final texture, pass the blended watermelon through a fine-mesh sieve to remove any pulp, though this is entirely optional.

In a large mixing bowl, beat the heavy cream using an electric mixer set to medium-high speed. Continue beating for about 6 minutes, watching closely as you near the end, until the cream forms soft peaks that hold their shape but still droop slightly at the tips. Be careful not to overbeat, as this will turn the cream into butter.

Take a separate bowl and combine the watermelon juice from the first step with the condensed milk, lime juice, salt, and vanilla extract. Whisk everything together thoroughly until the mixture is well blended. The lime juice will brighten the watermelon and balance the sweetness, while the salt enhances all the flavors and the vanilla adds subtle complexity.

Using a rubber spatula, carefully fold the watermelon-condensed milk mixture into the whipped cream with a gentle lifting and turning motion. Continue folding just until everything is combined and no white streaks of cream remain visible. Work gently to preserve the air you've incorporated into the cream, as this is what creates the light, creamy texture and prevents the ice cream from becoming icy. Pour the mixture into a freezer-safe container, cover, and freeze for a minimum of 6 hours or until firm enough to scoop. You can check the texture after 4 hours if desired, then return it to the freezer to finish setting.