Arrange the popcorn in a shallow layer on a large baking sheet, discard hard kernels and scorched pieces, then gather the remaining popcorn in a very large bowl. The sorted popcorn should look evenly popped, with no dark or unpopped pieces hiding underneath.

Place the butter in a large, preferably light-colored saucepan and heat it over medium. As it liquefies, its pale yellow color will be easy to monitor against the pan.

Stir across the bottom of the saucepan as the butter cooks. A foamy surface and small brown flecks underneath signal that the milk solids are toasting.

Keep the butter moving until it reaches a deep golden shade, watching closely as the color develops. A toasted, nutty scent should accompany the change from its earlier lemon-yellow appearance.

Reduce the burner to low, add the marshmallows, and stir until no unmelted pieces remain. The finished coating should look smooth and cohesive rather than lumpy or scorched.

Cover the popcorn with the warm marshmallow mixture and fold thoroughly with a rubber spatula. Look for a coating throughout the bowl rather than thick pockets of marshmallow between dry patches.

With hands lightly greased with butter or oil, gather the comfortably warm mixture into about six rounds using gentle pressure. Each ball should hold together without becoming a tightly compressed lump.

Allow the rounds to cool completely, then enclose them individually in plastic wrap and place them in an airtight container. They should feel set enough to handle without losing their shape.