In a large saucepan, add the whole milk. Turn heat to medium low and bring to a gentle simmer. Puree the watermelon and set aside.
In another bowl, whisk the egg yolks and the 1 cup of sugar together until smooth. Temper the eggs, by slowly adding about ¼ cup of the hot milk mixture in while whisking continuously. Pour the custard into the hot milk and place over low heat.
Stir the custard mixture for 5-7 minutes or until the mixture has slightly thickened (enough to coat the back of the spoon). Don't bring to a boil or the mixture will curdle.
Pour the custard mixture through a sieve into a clean mixing bowl and let cool to room temperature. Stir every 5 minutes. Stir in vanilla extract and salt. Once completely cooled, cover with plastic wrap and refrigerate a minimum of 4 hours to overnight.
Once the custard is cold, add heavy cream to bowl and mix until stiff peaks form. Gently fold the custard into the whipped cream with a spatula.
Stir together the pureed watermelon and sugar until the sugar has dissolved. Add this into the gelato base.
Pour the gelato into the loaf pan and place in freezer. After 45-60 minutes, whip it up to break up any ice crystals that have formed. Repeat this process 2-3x until it has thickened.
Cover well and store in the freezer for up to 2 months.