Place 10 cups of plain popped popcorn into a large bowl. Remove any unpopped kernels.
In a heavy-bottomed saucepan over medium heat, melt unsalted butter with salt, and vanilla. Add mini marshmallows and stir until completely melted and smooth.
Pour the melted marshmallow mixture evenly over the popcorn. Stir gently with a spatula to cover all the popcorn.
Lightly grease your hands with extra unsalted butter (or wet your hands with water or cooking spray). Quickly press portions of the mixture into balls about the size of a baseball.
Place the formed popcorn balls on wax or parchment paper. Let them cool completely, then store any leftovers in an airtight container at room temperature.
Enjoy your homemade popcorn balls as a fun snack for any time of day.