In a large saucepan, combine 6 cups of freshly popped popcorn, 2 cups whole milk, and 1 cup heavy cream. Heat over medium-low heat, stirring occasionally, until it just begins to simmer. Remove from heat, cover, and let it steep for at least 30 minutes.

Strain the infusion through a fine-mesh sieve into a large bowl, pressing the popcorn to extract as much liquid as possible. Chill this liquid thoroughly in the refrigerator for at least 2 hours.

In a medium saucepan, whisk together 1.5 cups heavy cream, 0.5 cup whole milk, granulated sugar, and salt. Heat over medium heat until the sugar dissolves.

In a separate bowl, whisk the egg yolks. Slowly ladle about half a cup of warm cream into the egg yolks while whisking constantly. Combine back into the saucepan with the remaining cream and heat until thickened.

Stir in vanilla extract and strain into the chilled popcorn-infused liquid. Chill the mixture over an ice bath until completely cold, then refrigerate for at least 4 hours.

For the optional caramelized popcorn, melt butter, brown sugar, corn syrup, and salt over medium heat. Bring to a boil, then add 3 cups of popcorn and stir to coat. Spread on a lined baking sheet and cool.

Churn the chilled base in an ice cream maker according to the manufacturer's instructions until thick and creamy.

If using caramelized popcorn, fold it into the churned ice cream before transferring to an airtight container. Freeze for at least 4-6 hours until firm.