Preheat oven to 300°.
Line a large sheet pan with parchment paper.
Pop popcorn with an air popper or on the stove-top in a large covered pot; set aside.
Combine butter, brown sugar, and corn syrup in a medium saucepan. Bring to a boil, stirring to combine. Allow mixture to boil for 3-4 minutes.
Pour hot mixture over popcorn and stir to coat. Pour popcorn onto prepared pan and spread to an even layer. Sprinkle with coarse salt.
Bake at 300° for 30 minutes, stirring every 10 minutes.