For the ice cream, in a 4 to 4 1/2 quart, heavy-bottomed saucepan, bring cream, milk, salt and butter flavor to a simmer over medium heat, stir constantly with a spatula to prevent scorching.
Remove from heat. Stir in 10 cups popcorn. Let cool for 30 minutes at room temperature, pressing on popcorn with a spatula several times to release flavor.
Meanwhile, use a blender to process remaining 2 cups popcorn until finely ground and powdery. Store covered until ready to churn ice cream.
In a 4 to 4 1/2 quart, heavy-bottomed saucepan, whisk together the eggs and sugar until smooth.
Strain cream mixture through a fine mesh strainer into egg mixture, pressing firmly on popcorn with a wooden spoon to release all liquid. Discard popcorn.
Cook over medium-low heat, stirring constantly with a spatula to prevent scorching until mixture reaches 160 degrees on an instant-read thermometer.
Pour mixture through a fine-mesh strainer into a large (4 cup) measuring cup or bowl.
Cover top of mixture with plastic wrap and refrigerate until very cold (minimum 4 hours).
Process cold cream mixture in ice cream maker according to manufacturer’s instructions, adding finely ground popcorn at end of churning.
Cover top of ice cream with plastic wrap and freeze until firm.
For the topping, in a 2 quart heavy-bottomed saucepan stir together the brown sugar, salt, cream and corn syrup until blended.
Bring to a simmer over medium-low heat, stirring with a spatula. Add butter and return to a simmer.
Gently simmer, stirring constantly over medium-low or low heat for 3 to 4 minutes or until sauce darkens slightly and thickens.
Cool at room temperature for 20 minutes or until slightly thickened but still easily pourable.
To assemble sundaes, freeze 4 dessert cups or bowls until very cold.
Place equal sized scoops of ice cream into cold dessert cups or bowls.
Drizzle with topping. To garnish, sprinkle caramel corn and butter flavored popcorn over the tops. Makes 4 ice cream sundaes