Place the blueberries, water, and sugar in a pot and bring to a simmer. Cook until all the blueberries have exploded into a purply sauce thick enough to coat the back of a spoon, but not necessarily as thick as jam. Set aside to cool.
While the blueberries are cooling, bloom the gelatin in 1 tbsp of the milk.
Place the rest of the milk, heavy cream, basil, and salt into a pot. Heat until steaming.
Add the bloomed gelatin into the milk mixture and stir until gelatin is dissolved. Then, take the mixture off the heat. Do not let the mixture boil.
Stir the blueberry sauce back into the mixture and add the vanilla.
Strain the whole concoction into a bowl or pitcher to get rid of basil leaves and blueberry skins. Let cool. You can keep this mixture in the fridge, covered, until ready to churn.
When ready, pour your blueberry ice cream mixture into your ice cream machine and churn according to the machine's instructions. I like to add in my 1/4 cup honey as the ice cream is close to being done churning, so I get some honey swirls that don't fully incorporate, but you can add the honey at any time.
Scoop churned ice cream into a container and freeze for at least two hours to firm up, or serve immediately at soft serve consistency.