In a heavy-bottomed saucepan, bring the maple syrup to boiling over high heat. Reduce the heat to medium-low; simmer until the syrup registers 220°F on a candy thermometer, about 5 minutes.
Stir cornstarch mixture into syrup; boil for 1 minute. Remove saucepan from heat. Stir in rum and walnuts. Let mixture cool completely.
Spoon into airtight jar. Store in refrigerator for up to 2 weeks.
