Pop the popcorn and transfer it to a large, heat-safe bowl, picking out any unpopped kernels. Set aside.

In a heavy saucepan, combine the brown sugar, corn syrup, and butter. Bring to a boil over medium heat, then reduce heat to medium-low and cook about 7 minutes. Add marshmallows and vanilla and stir until the marshmallows are melted. Remove from heat. Pour over the popcorn and stir quickly to evenly coat the popcorn.