Line bottom of 13x9-inch pan with cooking parchment paper.
In 3-quart saucepan, heat 4 cups of the marshmallows, the butter and salt over low heat about 8 minutes, stirring constantly, until melted. Stir in cereal until almost coated; stir in remaining 1 cup marshmallows. Using greased rubber spatula, evenly scrape mixture into pan and spread evenly. Refrigerate about 30 minutes or until easy to handle.
Turn pan upside down to remove cereal layer; discard parchment paper. Cut into 12 rectangles, 4x3 inches each. Working quickly, spread 1/2 cup of the ice cream onto 1 rectangle; top with another rectangle. Repeat to use up rectangles and ice cream. Freeze on parchment paper-lined cookie sheet at least 1 1/2 hours until firm. Wrap sandwiches individually in plastic wrap and store in freezer.