Swirl peanut butter into ice cream. Place in freezer 30 minutes or until firm enough to spread.
Spread 1/4 cup ice cream mixture onto each of 8 gingersnaps. Top with remaining 8 gingersnaps. Place sandwiches on a 15- x 10-inch jelly-roll pan; freeze until firm. Wrap sandwiches in plastic wrap, and store in freezer.
To soften ice cream in the microwave, remove top and liner (if any) of carton. Microwave on HIGH (power level 10) in 10-second intervals, checking in between, until ice cream reaches desired consistency.