Combine the cream, milk, sugar, and salt in a saucepan over medium heat. Bring to a simmer and stir until the sugar dissolves. Remove from the heat and stir in the vanilla.
While the ice cream base is warming, pop the popcorn in the microwave. Transfer 6 cups of popped corn to the pitcher of a blender, taking care that no unpopped kernels are in the pitcher with the popcorn.
Pour the warm ice cream base over the popcorn in the blender and let the popcorn soak in the mixture for a few minutes.
Blend the mixture until smooth and then pour through a fine mesh sieve into a container with a lid. Refrigerate for at least 4 hours, or overnight, until completely cold.
When ready to churn, pour the mixture into the ice cream maker. Churn according to the manufacturer's instructions. Transfer the finished ice cream to an airtight container and place it in the freezer until ready to serve. Serve topped with remaining popcorn and/or caramel sauce, if desired.
Notes
I use a "tender white butter flavored" microwave popcorn to make this ice cream. I don't recommend "movie theater butter" or "plain" popcorn for this recipe.